The best place to find a mammoth is in the snow biom if wanting to tame you will want a qwetzal to pick it up after it's done taming or bring a saddle for it to ride home and get levels but before taming this beast I would get a berry eater to get the berrys to tame it it's very cold so unlock fur armour and make it or else you will freeze to death out there bring your qutzele with lots of weight and Melle damage to protect your mammoth whilest it tames and weight to carry back to your base to keep it safe from predators around your place and then your done to go of and it's yours to keep.
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....)