Humans, climate change, impact events, or a combination of factors.
The short answer is that nobody knows for certain. Lots of theory and peer reviewed papers but no absolute certainties. Most died out 10,000 years ago, but one tiny population lasted on Wrangel Island until 1650 BCE
   Researchers have analyzed the stomach contents of well preserved carcasses of mammoths, woolly rhinos and ancient horses, as well as preserved feces. Those contained a similar variety of plants to the ones in the permafrost – mostly forbs. Previously their presence had been downplayed because they do not register significantly in the pollen record. However analysis of ice cores(200) from Alaska and the yukon revealed DNA of these plants. The DNA analysis also showed that the vegetation changed dramatically around 10,000 years ago, when the Arctic grew warmer and wetter, giving rise to the tundra we know today, dominated by grasses and woody plants.
"Most of the evidence suggests these large mammals disappear almost at the same time these vegetation changes were taking place,"
Let battle commence!