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 )
If you see one near a body of water get a aquatic animal and start shooting it with tranq arrows/darts while your in the water stay away from the land or the mammoth will try to attack you if your not on land then it won’t noticeonce it’s knocked feed it
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 :)
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
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!
If taming, its easiest to either tame on outskirts like everyone else said or take a fast, leveled up dino with you for protection. I used my rex I tamed right before it and I had my argentavis to take him home. They keep up rather well unless you're going through a jungle. Shoot it in its trunk for easiest ko (I used darts. On a low level mammoth it can take 2 darts with the rifle to take em down easily)