Gemara

(Beraisa - R. Meir): If a Bechor is sick due to excess blood, one may let blood, but only in a place that will not make a Mum;

Chachamim permit even in a place that will make a Mum, but it may not be slaughtered until it gets another Mum;

R. Shimon permits relying on that Mum to slaughter it;

R. Yehudah says, even if it will die, one may not let blood.

(R. Chiya bar Aba): They argue only about making a Mum in a Ba'al Mum;

R. Meir is Mechayev due to "Kol Mum Lo Yihyeh Bo";

Chachamim exempt. It says "Tamim Yihyeh l'Ratzon." (Since a Ba'al Mum cannot be (offered) l'Ratzon, the Lav of making a Mum does not apply.)

R. Meir expounds Chachamim's verse to exclude Pesulei ha'Mukdashim after Pidyon:

Chachamim expound R. Meir's verse to forbid causing a Mum;

(Beraisa): We read "Kol Mum Lo Yihyeh Bo" like "(Lo) Yehayei" (do not directly cause - Tosfos Yom Tov; Rashash - "(Lo) Yehayeh," there shall not be") a Mum;

Question: What is the source to forbid causing a Mum, e.g. sticking food to the ear (inciting dogs to eat the food, and thereby cut the ear)?

Answer: It could have said only "Mum". "Kol Mum" is extra, to equate making a Mum and causing a Mum.

34a (Mishnah - R. Eliezer): If one (a Kohen; R Gershom - or a Yisrael who keeps a Safek Bechor) pierced a Bechor's ear, it may never be slaughtered;

Chachamim say, it may be slaughtered when it gets another Mum.

Question (R. Yirmeyah): If Reuven pierced a Bechor's ear and he died, do we fine his son?

If the fine applies to the one who made the Mum, (after he dies) it does not apply to his son;

If the fine applies to the Bechor itself, it applies also to his son!

Answer (R. Zeira - Mishnah): If Reuven put fertilizer on a field in Shemitah, he may not sow it the next year;

(R. Yosi b'Rebbi Chanina): If he died, his son may sow it the next year;

This shows that the fine applies to the one who transgressed, but not to his son.

35a (Mishnah): The general rule is, any Mum made l'Daito (does not permit).

i. This includes a Mum that was (not directly made, but only) caused.

Avodah Zarah 13a (Beraisa): (After the Churban) if one was Makdish an animal, we lock it up so it will starve to death.

13b (Rava): We do not cut its legs, for that would look like blemishing Hekdesh.

Question: That is truly blemishing Hekdesh!

Answer: When the Mikdash stands, the animal is destined to be offered, it is blemishing Hekdesh. Nowadays that the animal cannot be offered, it is permitted.

Question: It should be forbidden, just like putting another blemish in a blemished Korban;

Even though the Korban cannot be offered, one may not blemish it further!

Answer: A blemished Korban cannot be offered, but it is redeemed and we offer a replacement with the redemption money. Nowadays, we cannot offer the animal or its value.

Rishonim

Rambam (Hilchos Isurei Mizbe'ach 1:7): If one blemishes Kodshim, e.g. he blinds the eye or cuts off the foreleg, he is lashed due to "Kol Mum Lo Yihyeh Bo." He is lashed only when the Mikdash stands, for then it could have been offered, and he disqualified it. Nowadays, even though he transgressed a Lav, he is not lashed.

Rosh (Bava Metzi'a 7:6): One may not blemish Kodshim through a Nochri even nowadays that the Isur is only mid'Rabanan, like it says in Bechoros 35a. This is due to the severity of Kodshim.

Terumas ha'Deshen (Pesakim 169): If a Yisrael commanded a Nochri to blemish a Bechor, there is no angle to permit slaughtering it based on this blemish, even if there are many Sefekos. A Gemara explicitly forbids it. However, if there is a Safek (whether the Yisrael commanded), and it is a Safek whether it is a Bechor, since the Isur to slaughter is only a fine mid'Rabanan, we are not as stringent as for a Torah law.

Poskim

Shulchan Aruch (YD 313:1): One may not blemish a Bechor.

Question: Avodah Zarah 13b connotes that nowadays, the Isur to blemish Kodshim is only mid'Rabanan. Rashi and Tosfos and the Rosh say so. Based on this, l'Chatchilah one may blemish a Safek Bechor nowadays and eat it with the Mum. The Pri Chodosh (OC 467:9) says so regarding Bal Yera'eh. Or, perhaps we may not, for the Rambam holds that also nowadays it is mid'Oraisa.

Answer (Chasam Sofer YD 306, cited in Pischei Teshuvah 1): Also according to Rashi, Tosfos and the Rosh we cannot be lenient about a Safek mid'Rabanan. The Isur mid'Rabanan is only because it looks like he blemishes Kodshim. Regarding shearing and working, we treat a Safek Bechor like a Bechor, because it is a Safek Torah. If so, if we blemish it, it looks like blemishing Kodshim. Normally, we may tell a Nochri to transgress something forbidden to us mid'Rabanan. The Rosh says that even nowadays we cannot blemish even through a Nochri, due to the severity of Kodshim. Why is there a severity of Kodshim? The Torah permits blemishing it! Every mid'Rabanan is permitted through a Nochri.

Note: Many Poskim say so regarding Mitzvos. I did not see anyone permit all mid'Rabanan laws through Nochrim.

Chasam Sofer: We must say that it is a disgrace, and looks like blemishing Kodshim. Many Takalos (transgressions) occurred through Safek Bechoros, yet no one permitted blemishing through a Nochri, and all the more so through a Yisrael.

Chasam Sofer (DH v'Ra'isi): Mayan Chachmah 64a supports Rashi, Tosfos and the Rosh. I do not understand how one can say that nowadays the Torah permits blemishing Kodshim, since they cannot be used themselves, and not their value. If so, why did Chachamim uproot the Aseh to tithe animals, due to Takalah? The Gemara suggested blemishing the entire herd. It would be better to leave the Mitzvah of tithing, and not forbid blemishing Korbanos nowadays! After tithing, one would blemish the Ma'aser, redeem it and throw four Zuz to the river and eat it with a blemish.

Note: There is no Pidyon of Ma'aser Behemah! Perhaps he holds that any enactment to belittle Kedushas ha'Guf must be accompanied by stringencies, like we find regarding the enactment to be Metamei the Kohen who did Parah Adumah - see Rashi Sukah 21a DH Mevi'in.

Chasam Sofer: If it was an early decree, we can say that Chachamim continued it even though it prevents fulfilling an Aseh. However, since the Isur mid'Rabanan to blemish began after the Churban, why did they decree?

Chasam Sofer (DH v'Tu): Also, why is this less (forbidden) than blemishing a Ba'al Mum? One who says that he will be a Nazir when Mashi'ach comes is forbidden to drink, for perhaps he will come today. Similarly, the Korban has potential to be offered! Also, we hold that one may offer Korbanos even without a Mikdash (because the Kedushah of Yerushalayim was permanent)! Only eating Bechor and Ma'aser depends on a Mizbe'ach. If we would petition the kingdom (ruling over Yerushalayim), we could build a Mizbe'ach there and offer Korbanos Tzibur, which may be brought in Tum'ah. The Tosafist R. Chaim Kohen wanted to go to Yerushalayim to offer Korbanos. Why was it clear to Rashi, Tosfos and the Rosh that nowadays there is no Torah Isur to blemish Kodshim?

Answer (Chasam Sofer): "Kol Mum Lo Yihyeh" applies to only when "Tamim Yihyeh l'Ratzon" applies. This excludes everything (that cannot be offered), both a Ba'al Mum and (even a Tam) nowadays. However, "Kol Mum" includes. R. Yochanan holds that one is not lashed for something included from "Kol", but there is an Isur (Torah) (Tosfos Pesachim 44a DH l'Inyan). Chachamim use "Kol" to include causing a Mum. R. Meir uses this to include a Ba'al Mum, and all the more so nowadays, which is more stringent than a Ba'al Mum when the Mikdash stands, like I explained. The Rambam holds like this. All this is according to R. Yochanan. Reish Lakish holds that what we include from "Kol" is only an Asmachta. In Avodah Zarah, Rava said 'it looks like blemishing Kodshim' to answer even for Reish Lakish. There is more reason to decree about a Ba'al Mum when the Mikdash stands than to decree about nowadays. He can say that Chachamim decreed not to tithe nowadays due to concern for an orphaned animal, like the Gemara (53a) suggested.

Shulchan Aruch (ibid.): One may not even cause a Mum, e.g. to put pressed dates on the ear so a dog will take it from there and cut the ear with it, or similar matters. One may not tell a Nochri to blemish it.

Chavos Ya'ir 33: A case occurred in which Tony, a Nochri friend of Reuven, was guarding Reuven's animal. Reuven had said that he intended to sell it to him; he did not have a chance, and it gave birth to a male Bechor. Tony was sure that Reuven would sell it, like he said, and castrated the Bechor. The Rosh forbids when a Yisrael's Nochri servant blemish a Bechor, for presumably he did so to please his master. Here is different. Tony did not castrate it to please Reuven. He was told to guard the animal from damage! However, there are reasons to be stringent. It is known that almost all Nochrim castrate males once shortly after birth. One may not leave a pregnant animal with them. This is unlike other blemishes. Castration improves it! This is causing a Mum, which we forbid, like putting pressed dates on the ear. Tosfos forbids giving things to a Nochri in a Chatzer (on Shabbos), for surely he will take them out. Here, since Reuven transgressed, we do not permit the Bechor, like R. Yerucham (168) says. Yisrael are not suspected of blemishing even a Safek Bechor, but they are suspected through a Nochri, for they think that this is permitted. We find (Beitzah 17b, brought in Beis Yosef OC 527 DH v'Im Avar) that Chachamim were more stringent about one who schemed than about Mezid. If the Nochri thought that it was his own, I would permit.

Shevus Yakov (2:92): If an animal is milking, we are stringent to consider the first child to be a Safek Bechor. Nowadays, the Isur to blemish Kodshim is mid'Rabanan, like Darchei Moshe (313:1, citing the Mordechai). Chachamim forbade slaughtering based on a Mum that was made intentionally; perhaps this is only for a Vadai Bechor. We cannot say so if the Yisrael made a Mum, for then the stringency has no effect. Everyone will blemish the Safek Bechor! However, if a Nochri blemished it, we can be lenient if it is unsure whether he did so l'Da'as a Yisrael (Terumas ha'Deshen), since it is a Safek Bechor, and especially if it was sold through money. (Some say that this suffices, but we do not rely on this alone.)

Shulchan Aruch (ibid.): If one overtly made a blemish or caused one, we do not slaughter it due to this blemish until it gets another blemish.

Beis Yosef (DH u'Mah she'Chasav v'Im): The Halachah follows Chachamim against R. Eliezer.

Shulchan Aruch (ibid.): If he (the owner, who blemished it) died, we do not fine his son (heir). He may slaughter it based on the Mum.

Shach (2): Chachamim fined only him, but not his son. Based on this, it seems that if he slaughtered it, b'Di'eved the meat is permitted to others.

R. Akiva Eiger: Tevu'os Shor (16:7) holds that the meat is forbidden even to others.