I've fought 4 Deer now, killed 2 and been KO'd twice.
My only successes were when "fought dirty": Once a deer was up against a cliff and I just kept hitting it until it died (I think it was trying to run away to do a charge, but kept eating cliff), and the other time a deer wandered up RIGHT next to my fence, and so I thought I'd try out the stomping trick.
I don't think I'll fight fairly against deer until I forge a sword for myself.