Chullin, Chapter 2, Mishnah 2. This chapter continues to examine the act of shechitah itself: how the cut is performed, and what happens when the shechitah is done in an unusual manner. Our mishnah takes up two such cases, one where a single slaughterer handles two animals at the same moment, and one where two slaughterers handle a single animal together.
Two animals in one act
"Hashochet shenei rashim ke'echad, shechitatan kesherah": one who slaughters two heads as one, his shechitah is valid. A person brought the knife across the necks of two animals in a single motion, and the mishnah rules that the shechitah stands.
Notice the wording. The mishnah validates what was done, which hints that this was not the ideal way to proceed in the first place. And indeed there is a case where slaughtering two at once is something one should avoid lechatchilah: korbanot. The pasuk uses the singular expression "tizbachehu", you shall slaughter it, teaching that a korban is meant to be slaughtered on its own, one at a time, and not paired with another. Still, the mishnah's point is that this is a directive about how to act properly, not a condition of the shechitah's validity. Once the shechitah has already been performed on both together, it is valid.
With ordinary animals, chullin, there is no such limitation at all. A person may deliberately slaughter two of them in one stroke, and it is permitted from the outset.
Two people, one knife
"Shenayim ochazin besakin veshochetim": two people take hold of the knife together and slaughter, "afilu echad lemalah ve'echad lematah", even if one is grasping it at the upper end and the other at the lower end, "shechitatan kesherah", their shechitah is valid.
One might have assumed otherwise. When two people grip a knife at opposite ends, the blade is liable not to stay level, and each of them may hold back and pull unevenly, so that the cut becomes hesitant rather than a clean, continuous draw. The mishnah teaches us not to be concerned for this. Two people slaughtering an ordinary animal together are permitted to do so, and we do not suspect that their joint grip will produce a faltering cut.
Here too, however, the leniency belongs to chullin. Regarding korbanot the standard is different. Just as one person may not slaughter two korbanot in a single act, so two people may not join together in slaughtering one korban. A korban calls for one slaughterer performing one shechitah.