In some of these cases, when two animals are slaughtered at the same time, the shechitah (slaughter) is valid. We're implying here that the shechitah is valid after the fact, but in the first place, a person should not slaughter two animals together at once. This applies specifically to korbanot (sacrifices).
The pasuk (verse) says, “you should slaughter it,” which tells us that one korban could be slaughtered at a time, not two. But what the Mishnah here is telling us is that even though, lechatchila (in the first place), that's the halacha (Jewish law), if somebody has already performed the shechitah, the shechitah is valid. But when slaughtering two regular animals, not korbanot, a person could slaughter two of them at the same time, and that is permitted lechatchila.
If two people are holding a knife together and slaughtering one animal at once, they're both doing it together. Even if one of them is above and one is below, and they're holding the knife at different ends, we say the shechitah is valid. You may think that if they're holding it at different ends, the knife is not going to be level and they're going to be moving with hesitation. What the Mishnah is telling us here is that we're not concerned about that. If two people are slaughtering an ordinary animal together, it's permissible; they're allowed to do it. We don't think they're going to be hesitant. But that's talking about ordinary animals, as we've stated. We're talking about korbanot. Just as one person is not allowed to slaughter two korbanot at the same time, here, two people are not allowed to slaughter one korban at one time. You need one person slaughtering one korban.