Gemara

(Rav Huna): If Shimon's animal was crouched in front of an idol, once Reuven slaughters one Siman, he forbids it.

He holds like Ula;

(Ula): Even though Reuven cannot forbid Shimon's cow by bowing to it, if he did an action to it, he forbids it.

Question (Rav Nachman - Beraisa): If one slaughters a Chatas outside (the Mikdash), for idolatry, on Shabbos (all b'Shogeg), he brings three Chata'os.

If cutting one Siman forbids, he would be exempt for slaughtering a Korban outside, for cutting the second Siman would be like cutting dirt (the animal was already forbidden)!

Answer (Mar Zutra): The Beraisa discusses Chatas ha'Of. Exactly half of the Kaneh was already cut. The moment he adds to this cut, the Shechitah is completed, so the liabilities come simultaneously.

(Rav Papa): Had Rav Huna not said that cutting one Siman forbids, we could not have challenged him from the Beraisa. He could say like Ula, that only a (major) action (i.e. complete Shechitah) forbids another's animal.

(Rav Nachman, Rav Amram, and R. Yitzchak): One cannot forbid another's property.

Question #1 (Mishnah): If two slaughtered together, and one intended to serve (a mountain, etc.), and the other intended for proper Shechitah, it is Pasul (no matter whose animal it is).

Answer: No. The case is, they are partners in the animal.

Question #2 (Mishnah): If Reuven was Metamei Shimon's Terumah or Kodshim or Menasech Shimon's wine (poured it for a libation to idolatry), if he was Mezid, he must pay.

Rejection: The case is, Reuven is a partner in the wine. (Directly, he forbids only his own share. However, one may not drink Shimon's share, since it is mixed with Reuven's.)

Suggestion: Rav Huna and Rav Nachman argue like the following Tana'im argue;

(Beraisa): If a Nochri was Menasech a Yisrael's wine not in front of an idol, the wine is forbidden;

R. Yehudah ben Beseira and R. Yehudah ben Bava permit it for two reasons. Nisuch is only in front of an idol, and one cannot forbid what is not his.

Rejection: Rav Nachman can hold like the first Tana. Only a Nochri forbids another's property. If a Yisrael was Menasech, we assume that he did not really intend for idolatry, rather to pain the owner of the wine.

Question (Mishnah): If two slaughtered together, and one intended for idolatry, and the other intended for proper Shechitah, it is Pasul.

Answer: The case is, the one with forbidden intent is a Mumar. (He is like a Nochri. He really would serve idolatry.)

Question (Rav Acha brei d'Rava): If Levi was warned just before he was Menasech Shimon's wine, and he replied 'I do so, accepting that I will be executed for this', what is the law?

Answer (Rav Ashi): The wine is forbidden. This is the ultimate case of a Mumar!

Avodah Zarah 59b (Rav Ashi): If a Nochri b'Mezid was Menasech Reuven's wine, Reuven may ask him for its full (initial) value.

The Nochri forbade it to Reuven. It is as if he burned it. Reuven collects payment for the damage, and not for the Yayin Nesech.

Support (Beraisa): If a Nochri was Menasech a Yisrael's wine not in front of an idol, the wine is forbidden;

R. Yehudah ben Beseira permits, because Nisuch is only in front of an idol, and one cannot forbid what is not his.

Rishonim

Rambam (Hilchos Avodah Zarah 8:1): If one slaughtered another's animal for idolatry or traded it for idolatry, it is not forbidden, for one cannot forbid another's property.

Rebuttal (Ra'avad): One can forbid another's property through an action, like Rav Huna taught. The Sugya in Avodah Zarah is like him. This refers to Yisrael Mumar or Nochri. If a regular Yisrael did so, we say that he merely wanted to pain the owner.

Rosh (2:14): Even though one who bows to another's animal does not forbid it, if he did an action to it (for idolatry), he forbids it. Rav Nachman (and Rav Amram...) say(s) that one cannot forbid another's property. Rashi explains that this is even through a major action, for we challenge this from Metamei and Menasech. R. Chananel says that they permit only if a small action was done. They agree that a major action forbids. With difficulty, we can say that (Metamei or) Menasech is not considered a major action, because the damage is not visible. Presumably, Rashi is correct. Even though one need not pay for unnoticeable damage, regarding Isur he did a great action. The Gemara concludes that Rav Yehudah (Ma'adanei Yom Tov - this should say 'Rav Huna') and Ula hold like the first Tana, unlike R. Yehudah ben Beseira and R. Yehudah ben Bava, but Rav Nachman's law is even like the first Tana. Only a Nochri forbids another's property. A Yisrael does not, even if he is a partner, for he merely intends to pain the owner. The Halachah follows Rav Nachman, for we establish his law like everyone. A Mumar, or one who was warned and accepted the warning, forbids another's property.

Ran (8b DH Garsinan): It seems that the Halachah follows Rav Nachman (and...), because the Sugya is like them. However, R. Chananel says that even they say that one cannot forbid another's property only through a small action. one can forbid another's property through a great action. Rashi holds that one cannot forbid another's property even through a great action. The simple reading of the Sugya is like this. Therefore, one who slaughters another's animal for idolatry does not forbid benefit from it. However, some forbid eating it. Even if one slaughtered another's animal for the sake of mountains, and he intended for a cure or similar matters, one may not eat it. Any association with idolatry forbids eating it. Regarding eating, we cannot say that one cannot forbid another's property. Here, he does not forbid it, rather, he does not permit it. It is as if it was not slaughtered, rather, it died by itself.

Poskim

Shulchan Aruch (YD 4:4): If a Yisrael slaughtered another Yisrael's animal for idolatry, he did not forbid it. Surely, he intended only to pain the owner.

Taz (4): The Ran says that some forbid eating it. He does not forbid it, rather, he does not permit it. It is as if it died by itself. Why didn't the Beis Yosef and Rema bring this? The Yam Shel Shlomo (2:22) brought it.

R. Akiva Eiger: What is the Taz' question? The Shulchan Aruch rules that one cannot forbid another's property, since he intends merely to pain the owner. Since he did not slaughter for idolatry, it was a Kosher Shechitah!

Bach (DH v'Ika): According to the Ran, what was the question from two who held a knife and slaughtered? The Mishnah said only Pasul. It did not say that it is Asur b'Hana'ah! It seems that since we forbid eating when one intended for a mountain, which is not idolatry at all, surely Shechitah for idolatry is more stringent, and it is Asur b'Hana'ah.

Taz (4): This is a poor answer. He did not investigate enough. The Ran holds that it is as if it he did not do anything, and it died without Shechitah. This applies only to one who slaughtered alone! Here, it is as if the other did a Kosher Shechitah alone!

Shulchan Aruch (ibid.): If he was a partner in the animal, some say that he forbids also the other's share, and some say that also here he intended only to pain his partner, and not to forbid.

Question (Shach 5): Surely, regarding his own portion he did not intend for pain. Therefore, presumably the same applies to the other's portion. Here, the Tur and Shulchan Aruch brought two opinions. In CM 385, they wrote Stam that if a partner was Menasech, he must pay.

Answer #1 (SMA 385:4): Regarding Yayin Nesech, he surely intended for idolatry. If he intended only to pain, he would have divided up and taken his share of the wine, and been Menasech only the other's wine! We cannot say so about an animal.

Retraction and Answer #2 (Drishah YD 4:3): This is unlike the Gemara, which asked from one to the other! Rather, in CM 385 the Tur and Shulchan Aruch merely teach about liability, without explaining in which cases one can forbid another's property.

Answer #3 (Shach 5, citing the Bach): They hold like the Ran, that regarding eating, one can forbid another's property.

Rebuttal and Answer #4 (Shach 5): This is astounding. The Ran said so only regarding one who slaughters l'Shem idolatry. He does not forbid it, rather, he does not permit it. It is as if it died by itself without Shechitah. This does not apply to Menasech! Also, the Tur and Shulchan Aruch connote that they totally permit. The Darchei Moshe explains like this, unlike the Ran. This is clear from the Gemara. According to the Ran, what was the question against Rav Amram from Shechitah on Shabbos? The Ro'oh holds like the Ran, and the Rashba refuted him. All the Poskim totally permit. Rather, even though there iare different opinions regarding Isur, the victim can say 'perhaps the Halachah follows the opinion that forbids Hana'ah. If you say that it is permitted, take the wine and sell it. I do not want to enter a Safek. Buy for me different wine in place of it!

Rema: If he was warned and accepted the warning, he forbids, like anyone who was Mezid.

Taz (5): What is the Chidush that if he accepted warning, he truly intended for idolatry? Even if he did not intend, Shechitas Mumar is forbidden! The Chidush is that it is Asur b'Hana'ah.

Shach (6): Whenever we discuss Shechitah for idolatry, this refers even to a tiny action.

Gra (5): Rav Ashi answered that one who was warned and transgressed is the ultimate case of a Mumar. This shows that he holds like Rav Nachman. Avodah Zarah 59b connotes that he holds like R. Yehudah ben Beseirah. If so, a Yisrael is no different than a Yisrael Mumar. Rashi and Tosfos there explained that really, he does not hold like R. Yehudah ben Beseirah. This is unlike the Ro'oh, who says that the Halachah follows R. Yehudah ben Beseirah due to the Sugya in Avodah Zarah (Rav Ashi holds like him).