You'd be surprised. You might eventually kill a deer, (and relatively quickly) if you hit the head or upper body, but not "instantly" unless you destroy major organs, preferably the heart. Which is fairly difficult to do at some distance, even with a modern rifle.
I mean, it would die otherwise, but it might also run away and you would never see it again or have to work hard to chase it.
We don't get to inflict bleed, though. Only NPC mobs.