Saber-toothed cats (also called saber tooth tigers) used to attack mammoths because the saber-toothed cats were carnivores, which means they ate meat (other animals). People used to think that the saber tooth cats would use their large canine teeth (which could be almost 2 feet long!) to break the neck of their prey, but more recently it's been revealed that the saber-toothed cats probably attacked their prey in other ways. This is because the saber-toothed cats are bulky animals -- their body probably looked more like a bear's body than a tiger or lion's body just because they were so bulky. It's also thought they hunted in groups, like lions do. So, it's thought they actually worked together to tear open the intestines of their prey or crushed their prey's windpipe, but didn't do something as quick as breaking it's neck. But it's really hard to know because these animals all went extinct about 10,000 years ago and these theories are mostly based on the animals' anatomy. For more information, feel free to check out these links:

Or read an article I wrote on giant extinct mammals of America: