Chullin, Chapter 2, Mishnah 4. This chapter has been working through the details that make a shechitah valid, and we already learned that both pipes, the windpipe (gargeret) and the food pipe (veshet), must be cut properly. Our mishnah takes up a case where the slaughterer got one pipe right and ruined the other one, and it asks what the status of the resulting carcass is.
The Four Cases
Begin with the first: "Shachat et haveshet", the food pipe was slaughtered as it should be, "ufasak et hagargeret", but the windpipe he ripped apart instead of drawing the knife across it. A rip of that sort is the invalidation known as ikur.
Next, the mirror image: "O shachat et hagargeret", the windpipe received a proper cut, "ufasak et haveshet", while the food pipe was torn.
Third: "O sheshachat echad mehen", he severed only one of the two pipes, "vehimtin lah ad shemetah", and then let so much time go by that the animal expired, reaching the remaining pipe only afterward.
Fourth: "O shehechlid et hasakin", he tucked the blade in, "tachat hasheni ufsako", beneath the pipe that was still uncut, severing it from that position after the first pipe had already been cut properly.
That last case requires a word of explanation. The cut has to proceed from the side of the pipe facing the animal's throat outward, in one continuous motion that moves from the first pipe to the second, which lies right beside it. Here the slaughterer went around to the far side and cut back from underneath. Burying the blade under the pipe this way is the disqualification called chaladah, literally hiding the knife.
Nevelah or Tereifah?
"Rabbi Yeshevav omer, nevelah": Rabbi Yeshevav rules that in all of these cases the animal is a nevelah, and a nevelah transmits tum'ah. "Rabbi Akiva omer tereifah": Rabbi Akiva rules that it is a tereifah, which does not transmit tum'ah.
Take the first opinion first. A nevelah is a dead animal, that is, any animal other than a kosher one whose death came through a valid shechitah. It may not be eaten, and it conveys tum'ah to a person who carries it. Rabbi Yeshevav holds that a kosher animal that died through a defective shechitah stands exactly where an animal that received no shechitah at all stands. Once the shechitah is not kosher, the carcass is a nevelah, with all the consequences of tum'ah that follow.
Rabbi Akiva calls it a tereifah, and a tereifah does not transmit tum'ah. In his usage, a tereifah is an animal carrying a defect that will eventually cause its death. Such an animal is forbidden to eat even when it is slaughtered correctly, yet the shechitah still accomplishes something: it keeps the animal from becoming a nevelah, so the carcass does not convey tum'ah. Applying that to our cases, Rabbi Akiva reasons that although the shechitah as a whole was flawed, the fact that one pipe was cut properly is enough to keep the animal out of the category of nevelah. It is a tereifah, and it does not transmit tum'ah.
The General Rule
"Klal amar Rabbi Yeshevav mishum Rabbi Yehoshua": Rabbi Yeshevav then stated a general principle in the name of Rabbi Yehoshua.
"Kol shenifselah bishchitatah, nevelah": if what went wrong is the slaughtering itself, the carcass has the status of nevelah. "Kol sheshechitatah kara'uy", but if the slaughtering was performed exactly as required, "vedavar acher garam lah", and the animal was rendered unfit by some other factor, "lipasel, tereifah", then its status is that of a tereifah.
The something else means a defect in the animal, the kind of flaw that makes it a tereifah. But when the failure is in the act of slaughtering, the animal is a nevelah.
"Vehodah lo Rabbi Akiva": Rabbi Akiva subsequently conceded that Rabbi Yeshevav was right.