Presumably there would have been a giant feast afterwards because the meat doesn't keep. Would have been fun to attend.
I'd be interested to see ancient solutions to this. For example, if you were to tie the mammoth down, you might be able to cut off a few legs and eat them, while bandaging up the mammoth to keep it alive for a week or so till you kill it and eat the rest.
The only thing I can think of would be luring one near a winter camp and killing it nearby, when it would be cold enough to keep or freeze.
Even if you could butcher the several tons of meat and get it dried or smoked in time, transport and storage would be huge problems.
It's enough of an ordeal to process a moose, with modern tools and machinery.