Can an elephant kill a man?

Answer 1

Only if he has a weapon.

Recall Hannibal the commander of the Carthaginian armies. In his march toward Rome with battle elephants, the riders were equipped with a large iron wedge and a maul. In the event an elephant panicked the rider was instructed to drive the wedge through his mount, in effect stopping it by killing it almost instantly.

Primitive man hunted mammoths and perhaps mastodons (very large Proboscidea--same order as elephants) with little more than spears and torches.

Answer 2

Yes, an elephant certainly has the physical capacity to do so.