While I really like the idea of large creatures...I don't think I'd described shooting arrows at a mammoth as "fulfilling." Either they are going to die too easily and it will be disappointing, or they will be too hard to kill and it will be frustrating.
The only way to kill a mammoth is with a spear, preferably thrown from a distance. I just have this imagine of ridiculously hacking at their legs with a sword, and either (I hope) getting trampled/thrown 20 feet in the air, or being ignored until they unclimactically run out of hitpoints and die.
It should work well enough with a warbow, if you don't hit bones the arrow will penetrate to the feathers. I do not see that spears will go so deep and you want deep penetration to hit vital organs.
Yes nobody hunted mammoths with bows in real life, it was extinct before the bow was invented, add that the war bows like longbow or composite bows was not invented until much later then you need something able to penetrate armor. You don't need a heavy draw to kill normal animals like moose.
A spear work well against large creatures because it's long reach, however the trunk on a mammoths will have even longer range.
Setting it fur on fire with a fireball might work, or might make it seriously mad.