Gemara

40a (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.

(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 or Menasech Shimon's wine, if he was Mezid, he must pay.

Rejection: The case is, Reuven is a partner in the wine.

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 someone else'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 to serve (a mountain, etc.), and the other intended for proper Shechitah, the Shechitah is invalid.

Answer: The case is, the one with forbidden intent is a Mumar.

Question (Mishnah): If Reuven was Metamei Shimon's Terumah, or was Menasech Shimon's wine, if he was Mezid, he must pay.

Answer: The case is, Reuven is a Mumar.

41b (Mishnah): If one slaughters a Chulin animal (outside the Mikdash), and says that it is an Olah, or any Korban that one may bring voluntarily, it is Pasul.

If two hold a knife and slaughter, and one intends for one of the above, and the other for a proper Shechitah, the Shechitah is invalid.

Rishonim

Rosh (2:14): The Gemara concludes that Rav Yehudah (this should say 'Rav Huna') and Ula hold like the first Tana, unlike R. Yehudah ben Beseira and R. Yehudah ben Bava, but the law of Rav Nachman, Rav Amram, and R. Yitzchak 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 them, for we establish their law like everyone. A Mumar, or one who was warned and accepted the warning, forbids another's property.

Rambam (Hilchos Shechitah 2:21): If two held the knife together and slaughtered, and one intended for something that forbids the animal (e.g. idolatry), and the other had no intent or the end for something permitted, it is forbidden. The same applies if they slaughtered one after the other, and one intended for something that forbids the animal. This is when the one who had forbidden intent was a partner in the animal. If not, it is not forbidden, for a Yisrael one cannot forbid another's property. He intended only to pain the owner.

Tosfos (41a DH b'Yisrael): Rashi explains that we established the Beraisa to discuss a Yisrael Mumar, and we could have established it to discuss a partner, like above. This is difficult. If so, why did the Gemara ask again questions that it already answered? Rather, even if he is a partner, we can say that he intends merely to pain the owner.

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.

Beis Yosef (DH Yisrael): The Poskim rule like Rav Nachman because the Sugya is like him. The Ran, Rosh and Rashba hold like Rashi, that one cannot forbid another's property even through a great action. The Rosh rules like the conclusion, that the Beraisos discuss a Yisrael Mumar. If he is not a Mumar, even if he is a partner, he does not forbid, for intends merely to pain the owner. However, the Rambam forbids when two slaughtered and one intended for idolatry, if he was a partner. If not, one cannot forbid another's property, for he intends merely to pain the owner. Why did he rule like the first answer, unlike the conclusion?! He must explain like Rashi, that we established the Beraisa to discuss a Yisrael Mumar, and we could have established it to discuss a partner, like above. However, now that we say that a Nochri forbids, we establish it to discuss a Nochri, according to the first Tana. Tosfos disagreed, for if so, the Gemara asked again questions that it already answered! Tosfos concluded that we can say that even a partner intends merely to pain the other partner. We can say that Rashi and the Rambam hold that the Gemara asked the questions again to show that now that we say that a Nochri forbids others' property, we can give another answer to the previous questions, i.e. they discuss a Yisrael Mumar. This is clear from Rashi's Perush. Do not ask why we establish them to discuss a Yisrael Mumar, and not a Nochri. Regarding one who was Metamei..., it says that if he was Mezid, he is liable. A Nochri would not abide by what Yisrael tell him! A Yisrael Mumar might repent and follow the law. Since they hold that we did not need to establish it to discuss a Yisrael Mumar, for we could have given the first answer, we are stringent like the first answer. Also, the Beraisa of Metamei is difficult according to the latter answer, for a Stam Yisrael Mumar does not follow the law. Also, the Mishnah of two holding the knife is difficult. If he is a Mumar, even if he slaughtered Stam, his Shechitah is Pasul! It is difficult to say that he was not a Mumar, and he became a Mumar during this Shechitah, e.g. they warned him during the Shechitah and he accepted the warning, like Rav Ashi answered. Obviously, that since he accepted death, he truly intended for idolatry. The Tana did not need to teach this!

Shulchan Aruch (5:3): If two slaughtered, whether they held one knife, or each held a different knife, and one intended for something that forbids (i.e. a Korban that one may bring voluntarily), it is Pasul. Similarly, if they slaughtered one after the other, and one intended for something that forbids the animal, it is Pasul. This is when the one who had forbidden intent was a partner in the animal. If not, it is not forbidden, for a Yisrael one cannot forbid another's property. He intended only to pain the owner.

Beis Yosef (DH u'Mah she'Chasav b'Shem): This is obvious, for if the Shechitah was finished through one with Pasul intent, it is Pasul. The Rashba says so. The Rambam says that if he is not a partner, one cannot forbid another's property. The Tur omitted this. Perhaps he relied on what he wrote in Siman 4, where he explained the Rambam, and said that the Rosh argues. However, the Rosh holds that even a partner cannot forbid another's property. The Mishnah of two holding the knife and slaughtering refutes him! Rather, he holds that 'one cannot forbid another's property' applies only to something forbidden letter of the law, because he intends merely to pain the owner. However, we forbid slaughter l'Shem (certain) Korbanos only due to Mar'is Ayin (lest people think that it is forbidden). Even if it is not his, one who sees will think that it is his, and might come to permit Kodshim outside the Mikdash! Therefore, it is forbidden even if he is not a partner. Even though it seems that also the Rambam forbids these only due to Mar'is Ayin, for he says 'it is like one who slaughters Kodshim outside', he holds that if has no part in it, he does not forbid. When someone slaughters another's animal for the sake of something Pasul, there is publicity (so no one will permit Kodshim outside).

Rema: Some forbid in every case, due to Mar'is Ayin. One should be stringent.

Taz (6): Even though the Kosher Shochet suffices to permit, since also the Pasul slaughters, he forbids. According to the Ran, it is as if the Pasul does not do anything. We should permit due to the Shechitah of the Kosher!

Taz (7): The Beis Yosef and Rema are astounding. We never find that Mar'is Ayin is more stringent than a real Isur! Also, why didn't the Tur mention that the Rambam and Rosh argue about this (one who slaughters another's animal l'Shem Kodshim)? I say that Tosfos and the Rosh argue with Rashi and the Rambam only regarding idolatry, for surely a Yisrael does not intend for it, rather, he intends merely to pain the owner. Surely a partner who slaughters Kodshim forbids, for he thinks that he does a Mitzvah! The Tur wrote 'when two hold the knife and one intends for Isur...' Regarding idolatry, according to the Rosh this refers to a Mumar, and according to the Rambam, it refers even to a Yisrael who is a partner. Regarding Shechitah l'Shem Olah, all agree that a partner forbids. If the animal is not his, we cannot say that he intends for a Mitzvah. One cannot be Makdish another's animal! There is no Mar'is Ayin. A partner is like a full owner. The Rambam mentioned a partner because it is different regarding Shechitah for idolatry. This is l'Halachah, but in practice, since the Beis Yosef and Rema are stringent, I say to be lenient only if there is another reason to be lenient, e.g. a mixture.

Shach (10): The Beis Yosef holds that here the Rosh agrees that a partner forbids, for he cannot intend merely to pain the owner. The Beis Yosef means that the Tur holds that the Rosh holds that even one who is not a partner forbids. Alternatively, the Beis Yosef agrees that the Rosh says so, but he rules like the Rambam.

Shach (9): The Bach is stringent if the Pasul slaughtered after the Kosher did enough for Shechitah. This is unreasonable. There is no room for Mar'is Ayin after a full Shechitah!