get on a nearby hill or rock and kill ones you don't want as they usually spawn in 2s or 3s (recommend an argentavis). then start shooting the mammoth with tranquillisers. when it torpor runs finish it off, they are very slow so very easy to hit. (protect from dire wolves, yutiranus, etc....)
Very easy to tame. They are just a bit slower than a human so you could just walk back and tranq. Run away once in a while because it does catch up while you are walking. Once your mammoth of choice is knocked just run away for 10 seconds and the rest will lose aggro. Mine just took down a low level alpha Rex and took about 1000 damage after I put 250 armour hat. It's got a good health pool anyways. It's better than the beaver in that it can defend itself and my base, it can hold much more wood. It also collects berries extremely well. Thatch is also not a problem with this. And on mobile it's water spray can knockback even a rex incase I gotta bail... Did I mention that it's faster than a rex? Only thing is that it doesn't get as much wood but in the Arctic there's plenty of wood. Just spend a few more minutes collecting wood is the solution...
Best way to tame is have a crossbow with butt load of tranq arrows walk backwards tranqing it as you go every now and then you need to turn around to get a bit further away. I know this works because i have three mammoths that i used this exact stratigy on
Don’t build a trap. All you need to do is shoot and run the’er really slow. And eventually they start torpor running so you just chase and shoot them till they fall over. I knocked out a lvl 115 and a lvl 95 that way at the same time Cause they both agrode on me. I probably should have killed one first.
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.
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 )