Playing on Genesis in the Arctic biome, and I built me a simple 3x3 trap out of stone foundations, stone stairs converted into ramps, and stone doorways. It might not want to get up the ramp, initially, and it's kinda slow, but it does hit hard, if you're just in fur. This one was lv90. Gonna try starve taming. But yeah, once it's in there, just keep popping it in the head with tranqs. It's big ol fat head sticks out above the trap, so you shouldn't have a problem with headshots. Hope this helps.
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....)