The more Eileen and I shoot monolithic bullets (of whatever brand) into big game the less I'm sure about what the minimum weight for certain game is.
So far the lightest bullets we've used on various kinds of big game are the 40-grain Cutting Edge Raptor at around 4300 fps from Eileen's .22-250 on a pronghorn doe at around 150 yards. It stood quartering toward her, and crumpled at the shot. We found the shank of the bullet under the hide at the rear of the far shoulder blade. (Raptors are designed to lose all their "petals," and this one did. Have never seen any difference in how Barnes X's that lost all their petals killed either.)
Eileen also instantly dropped an average cow elk at 120 yards, as it stood angling away, with a 100-grain TSX from her NULA .257 Roberts. But she has killed plenty of much heavier game with the 130 TSX and 150 Nosler E-Tip from her custom .308 Winchester, animals that many hunters still claim require at least a .300 magnum.
The longer I hunt the more I'm convinced that many hunters are convinced the harder a rifle kicks them, the "better" it kills.
