I've killed several whitetails with the 7.62x39, useing commercial ammunition and handloads. I never took a shot beyond 80 yards, and all were one shot kills. This was from a Ruger Mini-30. Finally traded the rifle, because it just wasn't very accurate. Groups ran about 4 inches at 100 yards with most commercial ammo, although some brands were buckshot type patterns instead of groups. One brand of Brazilian soft points did about 14 (yeah, fourteen!) inches at 100 yards.
I did everything I could think of with that rifle, tweeked the bedding, worked with a pressure point on the barrel, and a bunch of other stuff. I also tried just about every load combination you can imagine. Some of my best groups went two inches. For a sporter with a scope, from a rest, I just couldn't accept that level, and finally got tired of the rifle.