I just block its way with my wyvern and then place dino gates around it. Then I tranq it with arrows. When it's unconscious I place spike walls around the dino gates. After it's tamed I get my quetzal and carry it home. It's not hard. The only issue is the various predators in the snow biome. Clear the area before you start taming. Always watch out and guard the mammoth.
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.