You can kill just about any animal with just about any cartridge. When I hunted caribou with Inuits in northern Canada, they used 22 mags to kill caribou and thought all the center fires we had were too big. They would look at our guns, shake their heads, and say, "Too big shoot caribou." But when they kill a caribou, they run their canoes right up next to one that is swimming and shoot it right in the ear. So, that works for them.
The question you need to ask yourself is: How much do I respect the animal? By that I mean, please don't take a chance on wounding it because the rifle caliber you were using required an absolutely perfect hit. So many things can go wrong - a little wind, a slight movement of the animal just as you pulled the trigger, a tiny branch that you didn't see that was in the way, etc. You most likely won't be able to stick your barrel in its ear like the Inuits do, right?
My advice: stick with the recommended "usual" calibers for the game that you are hunting.