The word "mangle" means to mess something up by cutting, ripping, beating, or crushing it. For example, imagine what would happen to an animal that was attacked by a pack of wolves. The wolves would "mangle" the animal.
However, "mangle" is even more commonly used to talk about pronouncing something really badly. "Mangling" the pronunciation of a name, word, or sentence means pronouncing it really, really badly.
You can also "mangle" a song by singing it badly - singing it out of tune, forgetting lyrics, etc.