Chulin 2:1

If a person cut one pipe while slaughtering a bird or two when slaughtering an animal, the slaughter is valid. Cutting the greater part of a pipe is the same as cutting all of it. Rabbi Yehuda says the slaughter is only valid if he cut the veins in the throat. If a person cut half of one pipe when slaughtering a bird or one and a half pipes when slaughtering an animal, the slaughter is invalid; if he cut the major part of one when slaughtering a bird or the major part of both when slaughtering an animal, then the slaughter is valid.

Chulin 2:2

If a person slaughtered two heads simultaneously, the slaughter is valid (as sacrifices). If two people held a knife together while slaughtering the slaughter is valid; this is so even if one person held the knife from above and the other held it from below.