There's pretty serious debate about how, and even whether, early man hunted mammoths. There's not much evidence that humans actively hunted mammoths. Far as I've read, there are only two scant hints:
1. A tiny fragment of flint (probably from an arrow head or spear tip) found in the rib of a mammoth, but this was among tons of bones found in a site. Only one obvious sign of human attack was found among a mass of bones, far as I know.
2. A mammoth fossil with a spear stuck between its ribs. In an ironic twist, the spear was partially made from the tusks of a mammoth.
Maybe we just took advantage of dead mammoths. Maybe these two mammoths attacked humans first, and the wounds they got were in self defense (the humans probably got massacred). Who knows? I'm no expert, but even the experts disagree on whether or not we hunted mammoths. My opinion is thus:
We have definitive evidence that early humans paddled out into the ocean on boats and speared fucking whales. If we could do that, we could hunt mammoths. The more we discover about early humans, the more we learn that they were pretty damn smart then, too.