I’m pretty sure those aren’t intended for combat. Though, being able to kill with one is probably viewed as a perk.
Most axe combat, and even just using axes as tools, is based around momentum, building it quickly and maintaining it. Fortunately, the axe’s weight works in the combatant’s favor here.
Fair warning: neither of us are axe experts. I’ve use axes and hatchets extensively in Scouts; but, obviously, not on people. So neither of us know any of the more advanced techniques.
One handed axe strikes usually work by forcing the axe head into an elliptical path. The combatant will bring the axe up, then use the wrist or shoulder as a fulcrum to drive the axe into its strike vector. This can actually start with the blade being driven away from combat, only to flick it around and back into the opponent with little to no warning.
Two handed strikes usually work off building and maintaining momentum through multiple strikes.
A woodsman’s strike uses the combatant’s hands as a fulcrum. The strike starts with both hands placed far apart, one near the shoulder, and one near the knob. The combatant draws back, and as they strike they slide their hand down the shaft, closing the distance between their hands. This is strictly a one shot strike, though, as there’s no follow up, once the axe is imbedded in someone.
If the strike blows through someone, or reflects off a hard surface, you can regain control by moving the leading hand back up the haft, though this will also eat it’s momentum. I suspect that, with practice, you can simply whip the blade around into someone else, without completely killing it’s momentum, but I’m not sure of the logistics involved.
There was a historical technique for a bearded axe, that resembles a whip flourish. The axe would be swung in an “infinity” pattern. Starting over the shoulder, it would be driven down in front of the combatant, and back over behind their shoulder, it would then cross its path on the opposite diagonal. That said, the bearded axe had a six foot haft, so it handled more like a staff than a normal axe.