פירוש על חולין 53:82

One who slaughters [by cutting] two halves [of the simanim] of a bird, his slaughter is invalid (Hul. 2:1), and needless to say, [cutting] two halves of [the simanim] of an animal [is invalid]. Rabbi Yehuda invalidates any [slaughter] unless [the animal] is slaughtered [by cutting] the gullet and the two veins (i.e., the two major blood vessels in the neck). If he slaughtered half of the windpipe of a fowl and waited according to [the amount of time to perform a complete] slaughter, and afterwards completed the slaughter, his slaughter is valid. [If a slaughter involved the cutting of] one siman or the majority of one in a fowl, even though the it an extended period of time, the slaughter is valid. [If] there as a butcher who cut off the head in one swing, if he intended that [outcome], his slaughter is invalid, but if he did not intend it, his slaughter is valid. If the windpipe was severed and afterwards he slaughtered the gullet, his slaughter is invalid. If he slaughtered the gullet, and found the windpipe [already] severed, there is a doubt [whether the windpipe became severed] before he began the act of slaughter, and a doubt [whether it occurred] once the slaughter had begun. There was once such a situation, and they came and asked the Sages, and they said, "Every doubt involving a severed [organ renders the slaughter] invalid."