Gemara

(Mishnah): Chulin b'Azarah (slaughtered in the Mikdash) are buried;

R. Shimon says, Chulin b'Azarah are burned.

All Kodshei slaughtered Chutz li'Zemano or Chutz li'Mekomo are burned.

4b (Abaye): Wherever the Torah said not to do something, if one transgressed, he accomplished something. If not, he would not be punished!

(Rava): Wherever the Torah said not to do something, Iy Avid Lo Mehani (if one transgressed, it does not accomplish anything). He is punished for acting contrary to Torah!

6a Question: Practically, what do Rava and Abaye argue about?

Answer: They argue about whether Shinuy Koneh (if a thief acquires the theft through changing it).

Chulin 89a (Rava): Mitzvos Lav Leihanos Nitnu. (Fulfilling Mitzvos is not considered benefit, so it is permitted with Isurei Hana'ah.)

8a (Rav Nachman): One may slaughter with a knife of idolatry, for this is not benefit (the animal was worth more alive)!

(Rava): One may not slaughter with it a Mesukenes (dangerously sick animal), for he benefits by slaughtering it.

Pesachim 73a - Question (Ravina - Beraisa): If on Shabbos one slaughtered a Chatas outside the Mikdash for idolatry, he brings three Chata'os.

What did the Shechitah accomplish? (Why is he liable for Shabbos? The carcass is forbidden and Tamei because it was offered to idolatry!)

Answer (Rav Avira): It is not longer Ever Min ha'Chai. (It is now permitted to Nochrim.)

Rishonim

Rambam (Hilchos Avodah Zarah 7:19): If one slaughtered with a knife of Meshamshei Avodah Zarah (used to serve idolatry) a Mesukenes, it is forbidden, for this is beneficial, and he benefits from Meshamshim.

R. Gershom (33b DH R. Shimon): R. Shimon equates Chulin b'Azarah to Shechutei Chutz. Just like the latter must be burned because one deviated, also the former. We learn from "v'Chol Chatas Asher Yuva Es Damah" that whatever is done in the wrong place (with Kodshim, e.g. Shechutei Chutz) must be burned.

Rashi (33b DH Chutz): The Mishnah discusses Kodshim slaughtered with intent to eat or offer them in the wrong place or time.

Tosfos (4b DH Rava): If one slaughtered Pesach on (while he still owned) Chametz, Rava should say that the Shechitah was invalid! The Yerushalmi learns from a verse that it is Kosher.

Tosfos (6a DH v'Hashta): Why don't we say that Abaye and Rava argue about one who swore not to divorce his wife, and divorced her? Rava should say that she is not divorced, for he transgressed the Torah's will! Since the Torah did not make this Isur, rather, he himself made it, Rava does not say Iy Avid Lo Mehani.

Tosfos (73a DH Tiken): The Gemara did not answer that Shechitah is Metaher the animal from Tum'as Nevelah. This implies that Takroves (what is offered to idolatry) is Tamei mid'Oraisa. Avodah Zarah 52a connotes that the Tum'ah is mid'Rabanan! Rather, the Gemara answered that it removed the Isur Ever Min ha'Chai, to show that we cannot resolve from here that the Tum'ah of Takroves is not mid'Oraisa.

Poskim

Shulchan Aruch (YD 10:1): A knife of Meshamshei Avodah Zarah may not be used to slaughter a Mesukenes, for this is beneficial.

R. Akiva Eiger: We should say that since one may not benefit from the knife, this is like something that the Torah forbade, so even b'Di'eved it did not help. I.e. it is as if the animal was not slaughtered! Granted, when one slaughters another's animal for idolatry, most Poskim hold that according to the opinion that one cannot forbid another's property, one may even eat it. If so, it is not difficult why the Shechitah permits, since the Aveirah does not depend on Shechitah. Also Nechirah l'Shem idolatry is forbidden. Even if we would say that it was not Shechitah, he still transgressed. The Maharit asked why Shechitah on Shabbos helps. We should say that if he transgressed, it did not help. I answer that even if it was not a Shechitah, he transgressed (killing), and removed the Isur Ever Min ha'Chai, therefore 'Iy Avid Lo Mehani' does not apply. Here (Shechitas Mesukenes with a knife of idolatry), the benefit is that the animal did not die (without Shechitah). If we will say that it is not a Shechitah, it is as if it died by itself, and he did not transgress! The Turei Even (Rosh Hashanah 28a) says that even according to the opinion that Iy Avid Mehani says so only about Lavim. If the Hana'ah is a Mitzvah, e.g. blowing a Shofar of an Olah, if he was not Yotzei, he did not transgress, all agree that it did not help. If so, here we should say that it is not a Shechitah. This requires investigation.

Answer (Pischei Teshuvah 1): Pnei Aryeh (65) says that one may not benefit from the knife even to kill an animal (without Shechitah) in order to sell the meat to Nochrim. Therefore, even if we forbid the meat to Yisrael like Nevelah, he benefited from the knife. Therefore, we do not say 'what he did does not help.'

Tzelach (73a DH u'Letaretz): The Halachah follows Rava against Abaye with only six exceptions (and this is not one of them), that Iy Avid Lo Mehani. Therefore, a forbidden Shechitah is like Nechirah (it died without Shechitah). Why didn't the Gemara say that they argue about this? Rashi (in one Perush) said that they argue about Shinuy Koneh, i.e. if one transgressed Hash-m's will, whether it acquires (accomplishes anything). I say that this includes forbidden Shechitos. Therefore, the animal has Tum'as Nevelah.

Question: If one slaughtered Shechutei Chutz (Kodshim outside the Mikdash), or Chulin b'Azarah (in the Mikdash), or for Avodah Zarah, we should say that it did not help!

Answer (Noda bi'Yehudah 2 YD 9): The Torah says "Asher Yishchat ba'Machaneh". Since it calls Shechutei Chutz 'Shechitah', this shows that it is considered Shechitah, so it is not Metamei. Likewise, "Zove'ach la'Elohim" shows that Shechitah for idolatry is considered Shechitah. A Mishnah teaches that if one slaughtered Oso v'Es Beno (an animal and its child on the same day), Chulin b'Azarah, the latter is lashed for Oso v'Es Beno. I.e. it is Shechitah! There are two answers. Firstly, in Kidushin 57b the Gemara suggested that Chulin b'Azarah should be permitted b'Di'eved, and answered that "Ki Yirchak... v'Zavachta v'Achalta" teaches that you may eat (Chulin) only if you slaughtered it far from the Mikdash. If Chulin b'Azarah were Nevelah, we would not need a verse to forbid eating it! However, the Sifri expounds this verse to teach that we do not equate Chulin to Kodshim (and limit the time to eat Chulin to two days). Perhaps along with this, we expound that you may eat only what is slaughtered far away. In any case there is no proof that it is not Nevelah. Rather, I bring a proof from Kidushin 57b, in which R. Meir expounds 'just like Mine (Kodshim, slaughtered) in yours (outside the Mikdash) is forbidden, also yours (Chulin, slaughtered) in Mine (the Mikdash)'. The Gemara asked that if so, there should be Kares for Chulin b'Azarah! In any case the Hekesh shows that just like Shechutei Chutz is not Nevelah, also Chulin b'Azarah. All the more so it is not Nevelah, for there is Kares for Shechutei Chutz, but not for Chulin b'Azarah!

Noda bi'Yehudah: Rava said Iy Avid Lo Mehani only regarding Isurim that the Torah imposed, but not regarding what he himself forbade, e.g. if he swore not to divorce. Shechutei Chutz is forbidden only because he made it Hekdesh! However, if so, Tosfos (4b) had no question from slaughtering Pesach on Chametz.

Son of the Noda bi'Yehudah: He means that Rava's law is only when the Torah forbade the action. Rava admits when the Torah never forbade the action, and he invented the Isur.

Nachlas Tzvi (DH v'Da): Below (16:3), we say that if one slaughtered Oso v'Es Beno on the same day, one may not eat them! Even the stringent opinion forbids only on that day, due to a fine. Why don't we totally forbid, to fix the Isur? The Isur is only for a proper Shechitah (15:9)! This is all wrong, for if so, there is never an Isur of Oso v'Es Beno. The Torah said that it is a Kosher Shechitah! Tosfos (6a) says that we do not apply Iy Avid Lo Mehani to an Isur that one invented. The same applies to Oso v'Es Beno, for he created the Isur (through slaughtering the other today). The Noda bi'Yehudah holds that Rava's law applies when the Isur affects everyone, but not if he made an Isur to himself. If so, his law applies to Oso v'Es Beno. However, the Pri Megadim (Sifsei Da'as, brought below) answered this.

Shulchan Aruch (16:3): If one transgressed and slaughtered Oso v'Es Beno on one day, one may eat them. Some forbid (Rema - to eat the latter that same day).

Sifsei Da'as (3 DH v'Ra'isi): Iy Avid Lo Mehani does not apply to Oso v'Es Beno, since the Shechitah is not forbidden. Only the day is forbidden. In any case this is not difficult for Rava. Since the Torah taught that Mechusar Zeman (an animal that may not be offered yet) is forbidden to the Mizbe'ach, we infer that Mechusar Zeman (Oso v'Es Beno, which may not be slaughtered today) is permitted to people.