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 )