Alrighty guys, here was my adventure with taming a Mammoth. Level 2 Mammoth took me 20 minutes to tame, no narcotics (though I took some just in case), and 135 Azulberries. It was super easy but the only thing I had a problem with was the Rexs. So Mammoths are easy tames but you gotta protect them with your life once they're knocked out.
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....)