Chulin 1:2

If one slaughtered an animal using a sickle, a flint or a reed, the slaughter is valid. Anyone may slaughter, at any time, and with anything, except for a scythe, a saw, or one’s teeth and nails because these things (being serrated) tear rather than cut. If one slaughtered with a scythe by moving it forward only, Beis Shammai say that the slaughter is invalid but Beis Hillel rule it valid. If the teeth of a scythe are filed down, then it’s like a knife.

Chulin 1:3

If one slaughtered an animal by cutting the ring of the trachea and he left a hair’s width of its entire circumference, the slaughter is valid. Rabbi Yosi ben Yehuda said this is the case if he left a hair’s width of the greater part of its circumference.