The key part from below is "Quaternary extinction event of most of the Pleistocene megafauna that is widely believed to have been a result of human hunting pressure."
>Fossil evidence indicates that mastodons probably disappeared from North America about 10,500 years ago as part of the Quaternary extinction event of most of the Pleistocene megafauna that is widely believed to have been a result of human hunting pressure. The latest Paleo-Indians entered the Americas and expanded to relatively large numbers 13,000 years ago, and their hunting may have caused a gradual attrition of the mastodon population.
From https://en.wikipedia.org/wiki/Mastodon#Extinction
>Fossil evidence indicates that mastodons probably disappeared from North America about 10,500 years ago as part of the Quaternary extinction event of most of the Pleistocene megafauna that is widely believed to have been a result of human hunting pressure. The latest Paleo-Indians entered the Americas and expanded to relatively large numbers 13,000 years ago, and their hunting may have caused a gradual attrition of the mastodon population.
As far as megafauna and climate, see also https://en.wikipedia.org/wiki/Revival_of_the_woolly_mammoth#...