Obviously a mammoth is a little too big to just pop on your shoulders and carry back to the village, were the tribes mostly nomadic and just set up camp around the kill or did they have some system in place for transporting the carcass for butchering?
you should also try to ask this over at r/askanthropology but the current thinking is that the mammoth would be butchered where it fell. Bison (Bison bison), were much smaller and they tended to be butchered where they fell as well. There is a paper where they experimented by butchering a dead zoo elephant but I don't have my memory stick with me at the moment so I can't give you a reference, will try add it later