Gemara

(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, but he may not cut meat with it.

One may slaughter with it, for this is not benefit (the animal was worth more alive)!

He may not cut meat with it, for this improves the meat.

(Rava) Sometimes one may not slaughter with it. If the animal is Mesukenes (dangerously sick), he benefits through slaughtering it;

One may cut with the knife a nice section of a slaughtered animal, since it is worth more when it is whole, for one can honor an important person with it.

Question: Even without (the Isur Hana'ah of) idolatry, the knife absorbed forbidden fat!

Answer #1: The knife was used to cut wood for idolatry. (It never absorbed fat.)

Answer #2: Libun was done. (The knife was made glowing hot, to Kasher it.)

Rishonim

Rambam (Hilchos Avodah Zarah 7:19): If one slaughtered with a knife of Meshamshei Avodah Zarah (used to serve idolatry), the animal is permitted, for this is detrimental. If the animal was Mesukenes, it is forbidden, for this is beneficial, and he benefits from Meshamshim of idolatry. Similarly, one may not cut meat, for he benefits. If he cut in a destructive way, it is permitted.

Rosh (1:9): We forbid l'Chatchilah to cut meat with a knife of idolatry. "Lo Yidbak b'Yadcha Me'umah Min ha'Cherem" (you may not benefit at all from idolatry) does not forbid the meat b'Di'eved. This is unlike one who took wood from an Asherah (a tree planted for idolatry) and used it to heat a new oven, or bake bread in an old oven. Then, the new oven or bread is forbidden. If a stick from an Asherah was used to weave a garment, the entire garment is forbidden. It was totally made b'Isur. If one cut meat with a knife of idolatry, it was not totally made b'Isur. A proof is that we ask that even if the knife was not of idolatry, one may not cut with it, due to absorbed fat. If the entire meat were forbidden, this would explain why Rav Nachman taught about a knife of idolatry! The fat would forbid only at the place of the cut. Even if the question was why one may use it to slaughter or cut (a nice section), what was difficult? He must teach that the meat (except for what absorbed from the knife) is permitted. It is better to teach the greatest leniency, that even though l'Chatchilah one may not cut or slaughter due to the fat, b'Di'eved the (rest of) meat is permitted!

Rosh (ibid.): It is not clear whether a Mesukenes is like heating a new oven, baking bread or weaving a garment. Perhaps the animal would have died if it was not slaughtered, and there is great benefit here. Or, perhaps we forbid only regarding an oven, bread or garment, for they were made and finished through Isurei Hana'ah. A Mesukenes animal already grew. It lacks only a Heter to eat it through Shechitah. Even though Shechitah with Isurei Hana'ah benefits him greatly, Chachamim did not forbid b'Di'eved. This is reasonable. Avodah Zarah 62a proves this. If a worker was hired to work with Yayin Nesech, his wages are forbidden. The Gemara explains that this is a fine regarding Yayin Nesech. This shows that benefit from Isurim of idolatry does not forbid b'Di'eved. This was a special fine, lest people hire themselves to work for idolatry. Another proof is from Avodah Zarah 48b. It permits planting under idolatry in winter, but not in summer (when shade is beneficial). It does not say 'if one planted underneath, it is forbidden', even though the Reisha said 'if one passed underneath, he became Tamei.'

Poskim

Shulchan Aruch (YD 10:1): A new knife of Meshamshei Avodah Zarah, or an old knife without absorptions of Nochrim, may be used to slaughter a healthy animal, for this is detrimental.

Taz (1) and Shach (1): The new knife was used to service idolatry, but not for hot food, so there is no concern for absorptions.

Beis Yosef (DH Sachin): Rashi says that a healthy animal is worth more while it is alive, for it can produce children, plow and (eventually) be eaten. . One may not slaughter a Mesukenes, for this is beneficial.

Beis Yosef (DH u'Mah): The Tur brings from the Rashba that if one cut meat, he casts the benefit to the Dead Sea. The Rashba forbids Hana'ah until doing so. Casting the benefit to the Dead Sea suffices, for we hold like R. Eliezer, who says that this permits bread baked using wood of idolatry. Here, the benefit is the value of the cut meat above what it was worth before it was cut, i.e. the wages of the one who cut it.

Shach (3): Below (142:2), the Shulchan Aruch forbids l'Chatchilah. This is when he did not properly Kasher the knife.

Shulchan Aruch (ibid.): One may not slaughter a Mesukenes, for this is beneficial.

Taz (3): If one did so, the Tur brings from the Rashba that he must cast to the Dead Sea his benefit, i.e. the rental value of the knife to slaughter with it. The Rosh permits, because the animal already grew. The Maharshal says that we should rule like the Rashba.

Bach (4): The Rashba forbids the Mesukenes until casting money to the sea. If so, why did Rava say 'one may not slaughter', which connotes only l'Chatchilah? He said so for parallel structure to Rav Nachman, who said 'one may slaughter.' The Shulchan Aruch did not mention casting money to the sea. This connotes that he rules like the Rosh. However, the Maharshal says that the Rashba's opinion is primary.

Rebuttal (Shach 5): Below (142:2), the Shulchan Aruch discusses b'Di'eved. He explicitly forbids b'Di'eved! Also, here the Levush permits b'Di'eved, and in Siman 142 he obligates casting the benefit to the sea. Perhaps here they mean that the entire animal is not forbidden. This is difficult. I say that the Rosh brought proofs that the entire animal is not forbidden, i.e. it is unlike the bread baked using Asherah wood, which is totally forbidden. It does not help to cast money to the sea. The Rosh admits to the Rashba that here he casts the benefit to the sea. This is clear from R. Yerucham. The Tur, Beis Yosef, Maharshal and other Acharonim understood that the Rosh does not require even casting the benefit to the sea. This requires investigation. In any case the Ran, Maharshal and Bach rule like the Rashba, unlike the Mechaber below (who totally forbids. Casting the benefit to the sea does not help.)

Rebuttal (Pri Chodosh 4): The Rosh holds that in Avodah Zarah, we permit via casting money to the sea only when there is a mixture. Therefore, we must say that here the Rosh discusses totally permitting or totally forbidding. The Tur, Beis Yosef, Maharshal and Acharonim are correct. Below (142:2), the Mechaber cites the Rambam, and says that a Mesukenes slaughtered with a knife of idolatry is forbidden, i.e. totally. They hold that casting money to the sea helps only for a mixture. If one cut meat, it is forbidden. The Gemara asked why Rav Nachman permits l'Chatchilah. Even if there is no Isur of idolatry (since cutting is detrimental), it should be forbidden due to the fat. Rav Nachman should have said 'if he slaughtered, it is permitted.' Rashi explains like this, unlike the Rosh.

Hagahos ha'Bach (on the Rosh, 4): The Rosh holds that if Rav Nachman forbids (cutting meat) even b'Di'eved, when he permits, also this is (only) b'Di'eved. (It is as if Rav Nachman said 'if he slaughtered, it is permitted.')

Pleisi (3): The Pri Chodosh erred. The Rosh distinguishes between benefit of the bread and of the knife. The Shach explains that regarding the knife, we need only the rental of the knife to slaughter. If so, there is no proof from bread! However, if so, what was the Gemara's question? Due to absorptions, it suffices to peel off a layer. Due to idolatry, we require (casting to the sea) the rental of the knife! For a Mesukenes, this is a lot! Rather, this shows that Chachamim did not fine. I suggest that it is a Mitzvah to do Shechitah and not Nechirah (other ways of killing it through the Simanim). We bless on Shechitah. Mitzvos Lav Leihanos Nitnu. (Therefore the Isur Hana'ah of idolatry does not apply to Shechitah.) This is why the Rif omitted the entire teaching about a knife of idolatry. It was taught before Rav (this should say 'Rava' - PF) retracted (Rosh Hashanah 28a), and held that Mitzvos Leihanos Nitnu. We hold like his conclusion, that Mitzvos Lav Leihanos Nitnu, so the entire teaching is obsolete.

Note: In any case the Rif should have taught about cutting meat, which is not a Mitzvah!

Rebuttal (of Pleisi - R. Akiva Eiger): In Eruvin (31a), the Gemara permits using Isurei Hana'ah for an Eruv only if we say that one may make an Eruv only for a Mitzvah. If we say so, Mitzvos Lav Leihanos Nitnu applies. If one may make an Eruv for Reshus, one may not leave the Techum without an Eruv, and an Eruv saves him from Isur, but even so it is called Hana'ah. The same applies to Shechitah, since he slaughters for Reshus.

Rebuttal (of Pleisi - Nachalas Tzvi): How does the Pleisi understand the Poskim who bring the teachings about Shechitah with a knife of idolatry, even though we hold that Mitzvos Lav Leihanos Nitnu? Rather, Mitzvos Lav Leihanos Nitnu applies only when the only Hana'ah is fulfilling the Mitzvah. Here, he also benefited that the animal did not die (without Shechitah). This is unlike a Shofar of an Asherah (perhaps this should say 'Olah' - PF). There, without the Shofar, he lacks only the Mitzvah. Here, the knife gives also physical benefit. One who vowed not to benefit from a spring may immerse in it only in winter, but not in summer.

Nachalas Tzvi: Zichron Yitzchak (75) uses the Pleisi to support the Ba'al ha'Ma'or (Rosh Hashanah 7b), who says that Mitzvos Lav Leihanos Nitnu permits only a Torah Mitzvah like Shofar of Rosh Hashanah, but not a Mitzvah mid'Rabanan like Shofar of fast days. He learns from Shechitah. The Torah Mitzvah is to slaughter the majority of the Simanim. Mid'Rabanan, one must slaughter the entire Simanim. The Isur to slaughter a Mesukenes is due to this, for Mitzvos Lav Leihanos Nitnu does not apply to the last minority of the Simanim.

Rebuttal (Nachalas Tzvi) The Isur to slaughter a Mesukenes is because he benefits that it does not die without Shechitah. This is why one may slaughter a healthy animal. He does not benefit from the last minority of the Shechitah. In any case it is permitted through the majority!

Shulchan Aruch (142:2): If one slaughtered with a knife of Meshamshei Avodah Zarah, the animal is permitted, for this is detrimental. If the knife is new, or it is old and Libun was done, it is permitted l'Chatchilah. If the animal was Mesukenes, it is forbidden, for this is beneficial, and he benefits from Meshamshim of idolatry. Similarly, one may not cut meat, for he benefits. If he cut in a destructive way, it is permitted.