Once you knock down a mammoth give it tons of berries then go back to your home even if you don't live in the north. When tamed there's a button when in your inventory that says how many games you have. Find your mammoth in the list click request then soon your mammoth will teleport to you (I play on IPad so not sure if it will work on other platforms).
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.