You've probably already figured out what's wrong with the picture above: That's right, even cavemen wouldn't be stupid enough to sit there and get half of their own number killed trying to take on a hairy monster like that with deer walking around for the taking as they always have. "Scientists" claim that Indian ancestors wiped out not only all mammoths, but all other American megafauna as well in such a manner. In reality, the little bow which the image shows one caveman to have made out of a stick would be doing well to fire an arrow a little faster than he could throw it, and the arrow wouldn't get past the mammoth's fur and subcutaneous fat.
The weapon shown above is a typical Turko-Mongol bow, the ultimate weapon in warfare for the thousand year period between the huns and the development of useful firearms in Europe. The center part of the bow does not move much when drawn; the ears are doing most of the work and behave something like the cams in a modern compound bow, most of the stored energy being transferred to the arrow. The bows were of laminated wood and animal horn and heavy, and were drawn with thumb-rings as shown which were much like modern release devices, the grooved part of the ring being locked over the bow string and the thumb snapped loose from the two fingers over it to shoot. These bows were as far above the caveman's little stick bow as a Maserati Bora is above a horse.
Kublai Khan's soldiers faced elephants in Indochina with these bows, and the reports indicated that they managed to turn the elephants and panic them so that they fled and ran over their own troops in the rear. If any died from such wounds, they didn't die immediately. These, of course, were the smaller Asian elephants, with nothing like a mammoth's fur to protect them. The big question, of course, is how in the world is Alley Oop supposed to kill the mammoth with his little stick bow when Mongol archers, the best in the world, couldn't gaurantee kills on little Asian elephants with their awesome bows?
A heavy modern compound bow with hard cams and preformed limbs of modern composite materials firing glassy smooth arrows with surgical steel points honed to razor's edge is generally regarded as mandatory for hunting African elephants or rhinos. Archers approach to within 20 yards and then try to place a shot between two ribs, since a rib would prevent the shot from doing lethal damage. If the archer makes any noise, steps on a twig, breathes too hard, ends up upwind, or screws up in any way, he's in serious trouble. Moreover, the job is obviously one for one or two very competent bowhunters; any more people than that would guarantee an attack from the prey animal. Moreover, in the case of a mammoth, which had two feet of matted fur and then a layer of fat under the skin, there would be no possibility of seeing ribs to try to shoot between.
A well placed shot with a modern razorhead arrow fired from such a bow might have a shot at killing the mammoth shown above, if the hunter somehow managed to place a shot between ribs by sheer dumb luck. How long it would take him to die or how many of your crew he would kill before he died... that's another question. Little whitetail deer sometimes take half an hour to die from shots which pass cleanly through their chest areas.