We learned earlier that for Shechitah (slaughter) to be valid, both the windpipe and the foodpipe have to be slaughtered properly. Here, we're talking about a case where one of the pipes was done correctly, but the other one was cut in an invalid manner. The Mishnah says: Somebody cut the foodpipe properly, but he tore open the windpipe. Tearing it open is a disqualification of ikur (uprooting). Or he cut the windpipe properly, but tore the foodpipe. Next case. Or he cut one of the pipes and waited until the animal died, and then he cut the second pipe. Or, after cutting the first pipe properly, he took the knife, hit it under the second pipe, and cut it from there. In other words, when you're cutting, it always has to be from the inside of the throat, in a motion that goes from one pipe to the next, very close to it. So here he went all the way to the other side of where the original cut was, and he cut from that side. This is a problem of chaladah, hiding it. By making this type of cut, the slaughterer is hiding the blade under the pipe. When a person slaughters, he always has to cut the pipe from the side closest to the animal's throat to the far side. So here he did it wrong.
Rav Yishvav omer neveilah. Rav Yishvav says that in these cases, the animal becomes a neveilah, which transmits tum'ah (ritual impurity), and Rabbi Akiva omer tereifah. Rabbi Akiva says that it's a tereifah, which does not transmit tum'ah. Let's do the first opinion first. A neveilah is a dead animal, except a kosher one that died by shechitah. It is not allowed to be eaten, and it transmits tum'ah to people who carry it. According to Rav Yishvav, the kosher animal here died with invalid shechitah and is like one that died without any shechitah at all. As long as the shechitah wasn't kosher, it's considered to be a neveilah, and therefore it transmits tum'ah.
According to Rabbi Akiva, it's a terefah, which does not transmit tum'ah. According to Rabbi Akiva, a terefah is an animal with a defect, which is eventually going to die because of that defect. A terefah is not allowed to be eaten, even if it is slaughtered properly. But shechitah prevents it from becoming a neveilah, and the dead body would not transmit tum'ah. So, in the cases of our Mishnah, even though the shechitah was not done properly, Rabbi Akiva says that since one pipe was done properly, it's enough to prevent it from being called a neveilah. It's a terefah, which does not transmit tum'ah.
Rabbi Yishvav stated a general rule in the name of Rabbi Yehoshua: Any situation where the shechitah was invalid is a neveilah. Any other situation where the shechitah was fully valid, but the disqualification happened through something else, like a defect of the animal, which would make it a terefah. But if the shechitah was not done properly, then it's considered to be a neveilah. Rabbi Akiva later admitted that Rabbi Yishvav was correct.