They aren't extremely fast and are easily outrun, so just shoot it with a crossbow using tranq arrows and turn around and runa. Few steps when it gets too close. ( may be best to take out any other mammoths before attempting to tame )
On the raft build a 3x3 foundation with 3 walls high and a ramp going up into the raft. Go to the winter area youll find Mammoths there. Get it into the raft. Once in the raft shoot it with tranq arrows. Starve it and then feed. Kibble is 80times its food.
I tamed a level 40 mammoth, no cheats/tame boost on settings. It ate 100 mejoberry (it said 250 on here) but I needed 102 because spoil times a bummer. It also took 7 narcotics not 76 like it said here. Unfortunately didn't pay attention to how many tranq arrows it took. Hope this helps :)
Tame on the outskirts of the winter biome close to the ocean, there’s more visibility and you only have to watch for threats from one direction. Helpful because these guys take a long time to tame and everything in the winter biome is aggressive to them!
Build a raft with about 9 or so foundations/ ceiling and put Walls on the perimeter and ramps in the front and put large storage boxes along the walls and go to the swamp with a buddy and just sit on the mammoth on the front of the raft and swing away. Best wood/thatch/shroom farm ever