Chulin 2:3-4

Chulin 2:3

If, while slaughtering, a person severed the head with a single stroke, the slaughter is invalid; if the knife was twice as long as the neck, then it is valid. If one severed two heads with a single stroke, then if the knife was twice as long as one neck, the slaughter is valid. This is the case when the one slaughtering moved forward but not back, or backward but not forward; if he moved both forward and backward, no matter how little, even with a scalpel, then the slaughter is valid. If a knife fell and slaughtered an animal, even if it did so in accordance with the halachic parameters, the slaughter is invalid as per Deuteronomy 12:21, “you shall slaughter... and you shall eat,” i.e., we may eat that which we slaughter (actively, not passively). If a knife or one’s clothes fell and he picked them up (completing the slaughter through this action), if he sharpened the knife (without interrupting the slaughter), or if he got tired so another person came and completed the slaughter, then if the delay was long enough to slaughter such an animal, it is invalid. Rabbi Shimon says it is invalid if the delay was long enough for one to examine his knife.

Chulin 2:4

If a person cut an animal’s esophagus and then severed its trachea, or if he cut the trachea and then severed the esophagus, or if he cut one of them and waited for the animal to die, or if he stuck the knife underneath the second pipe and cut it, in all of these cases Rabbi Yesheivav says the animal is a neveila (which conveys ritual impurity), while Rabbi Akiva says it is a treifa (which does not convey ritual impurity). Rabbi Yesheivav stated a general principle in the name of Rabbi Yehoshua that whatever is rendered unfit through slaughter is a neveila, while whatever was slaughtered properly but was rendered unfit by something else is a treifa. Rabbi Akiva agreed with this.