I've only, purposefully, taken on a mammoth once. Best way to raise your bow is sneak attack, there is a perk on the sneak tree that gives you 3 times damage from sneak attacks. There is also a dagger perk which gives you 15X dagger damage from a sneak attack. (all in the sneak tree) When not going for sneak kills I use dual ebony war axes instead of my blade of woe (A really awesome dagger)
Yeah I upgraded my blade of woe to "epic" and I'm using ancient shrouded gloves so when sneak attacking with my dagger I get 30X damage.. kills alles one shot..