I would be extremely reluctant to try to kill a beaver with a 760, it just isn't enough. You might kill one with a perfect hit, but can you always deliver a perfect hit?
As for lighter stuff, I would use pointed or round nosed pellets for good penetration. I have killed bunnies at close range with b-b's because the gun was loaded with them to chase away bunnies & squirrels. A couple of garden-munching bunnies were close enough to whack with a b-b (10 pumps), but I would have loaded a pellet if I had one with me.