A new mishnah! What happens if the animal doesn't bleed at the time of shechitah? Apparently, that's a kosher shechitah. And one's impure hands won't render the meat impure (unless the slaughtering itself made it susceptible to impurity, and not just the liquid of the blood). The Gemara reexplains the mishnah to explain that the mishnah could not be talking about sacrificial foods, with several follow-up points to make the case that much stronger. Also, the Gemara delves into the impure hands, and what degree of impurity they may carry. Plus, the case of someone who purifies his hands and then exposes them to impure hands again - depending on how much exposure his whole body received, it may make a difference for what degree of impurity do his hand carry.