A new mishnah! One who slaughters an animal in the name of worship of natural bodies (mountains, rivers, seas, etc.), then the slaughtering is not kosher shechitah. Even if two people are doing the slaughtering together and one of them has correct "kosher" intent, the shechitah is still not valid. But it's also not fully idolatry either - except for a beraita that presents comparable cases as being idolatry (with slight differences that make room to say they are different). Also, if one's animal is lying in front of idolatry, then the moment one cuts that animal, it's prohibited - because it smacks of idolatry, even if it was not intended as such (live, the animal isn't a concern of idolatry, or not until a physical act is done to it). But does that really work? To make another person's animal problematic? The distinction is drawn between a "zevach" (or a shelamim/peace-offering) and a "chatat" - sin-offering.