Never seen it don, but have heard much of "barking squirrels."
This is done by shooting the limb under the squirrel, the wood fragments stunning the squirrel. The stunned squirrel is dispatched by swinging him by the hind legs and cracking his head against the tree truck. This leaves the head intact and the brains undamaged.
Incidentally, my cousin went to an auction, this around 1960 or so, and a squirrel rifle came up. When nobody bid on it, he offered a quarter. He bought the rifle, a .44 caliber, for twenty-five cents! I gave him a piece of scrap brass to make the missing trigger guard.