Mutter These are words usually said so no one can hear them, or so the intended person cannot hear. This could be used to say something bad about someone, but you don't want them to know what you have said. Murmur This is similar to a whisper. You can murmur something to your friend so nobody else can hear it. Mumble This is used to describe somebody saying something that nobody could understand. A child may mumble words if he is being scolded by his parents or teacher. Someone may also mumble words if they are drunk.

Mumble doesn't have to be used just for speech that no one can understand - it is also used for someone speaking carelessly, like they are not enunciating their words. Not necessarily making them gibberish, but just being sloppy with their words (in a quiet way).