So long as you can survive the encounter, if you inflict any kind of decent wound, wouldn’t the animal eventually die due to blood loss or infection? Not at metal as an immediate kill, but whatever works.
Even hitting vitals won't be "immediate", you'll still have some hectic moments/minutes dodging the thrashing mammoth. But if you don't strike a mortal blow the danger is much greater because the animal won't weaken and slow down. Instead it'll get pissed and probably fight back even harder.
