Mammoths had few predators because of their large size and protective social groups. It is likely that large carnivores of the time (like Smilodon) carried off very young or very old members of a mammoth herd.
The biggest predators of mammoths were humans. Humans lived in direct contact with mammoths about 12,000 years ago. From excavation of the areas where these human hunters lived (called Clovis sites) and from cave paintings, scientists know that humans hunted and killed mammoths.