Real men wrestle them to the ground and tear their throats out with our teeth.
Re wrestling to the ground and tearing with teeth - This may have been done, and regularly too.
Humans have certain physical advantages vs most prey animals - we have far greater endurance than most all of them, greater ability to shed excess heat, etc. The Olympic sport that may be closest to what humans were designed to do is possibly the marathon race.
One speculation is that the original human animal-level hunting technique on the African plains was simply to chase an animal to exhaustion.