"Most mammoths died out at the end of the last Ice Age. A definitive explanation for their mass extinction is yet to be agreed upon. However, the small mammoths of Wrangel Island became extinct only around 1700 to 1500 BC.
Whether the general mammoth population died out for climatic reasons or due to overhunting by humans is controversial. Another theory suggests that mammoths may have fallen victim to an infectious disease. A combination of climate change and hunting by humans is probably the most likely explanation for their extinction.
New data derived from studies done on living elephants and reported by the American Institute of Biological Sciences (BioScience, April 2006, Vol. 56 No. 4, pp. 292-298) suggests that though human hunting may not have been the primary cause toward the mammoth's final extinction, human hunting was likely a strong contributing factor. Homo erectus is known to have consumed mammoth meat as early as 1.8 million years ago.
However, the American Institute of Biological Sciences also notes that bones of dead elephants, left on the ground and subsequently trampled by other elephants, tend to bear marks resembling butchery marks, which have previously been misinterpreted as such by archaeologists.
The survival of the dwarf mammoths on Russia's Wrangel Island was due to the fact that the island was very remote, and uninhabited in the early Holocene period. The actual island was not discovered by modern civilization until the 1820s by American whalers. A similar dwarfing occurred with Mammoths on the outer Channel Islands of California, but at an earlier period. Those animals were very likely killed by early Paleo-Native Americans, and habitat loss."
http://en.wikipedia.org/wiki/MammothI haven't seen any evidence either way, and will refrain from putting forward any speculation until I do.