Actually bullets do kill by kinetic energy , or more precisely the transfer of kinetic energy in creating a wound channel.
I'll make this basic explanation, When bullets move, they have momentum. The faster they move and the heavier they are, the more momentum they have. Even though bullets are tiny, they have lots of momentum because they go so fast, relative to their mass. They also have huge amounts of kinetic energy, which they get from the chemical energy of the burning gunpowder. Bullets do damage when they transfer their kinetic energy to the things they hit. The faster something loses its momentum, the more force it produces. A rifle bullet coming to a stop in a tenth of a second produces as much force as a heavy, slow moving truck coming to rest in 10 seconds. That large transfer of kinetic energy makes a primary and secondary wound channels. primary and secondary wound channels are more recently and correctly called permanent and temporary cavitation channels, but i think, from that point, we all know what happens. there is no need to discuss hydrostatic shock.
bullets, lead or copper jacketed in any configuration, do not kill by cutting.