Different animals will give different amounts of cuts, although NPCs seems to constantly give around 20 cuts per person. Large animals, such as elk or bears can give up to 600 cuts per animal, more than enough for a whole season. Cuts from different animals have different nutrition levels, and so a cut from a pig will fill more hunger than a cut from a squirrel. To obtain meat from a dead animal, press # for the Extended Commands window then c to "Cut a carcass for meat."
Version 315p1: minimum 30 cuts per person. And now press E to open extended commands. After drying or smoking, meatcuts and fishes are reduced in weight, though still keep their nutrition level. Salting doesn't change weight.