Mutter and mumble are very similar, as they both mean to talk quietly and indistinctly. Murmur is slightly different, as it means to speak very quietly but not necessarily indistinctly. Mutter and mumble can also be used to describe someone who is complaining in a very long and unclear way. 'He was muttering/mumbling about the new parking restrictions.' In this case, you could probably hear the words they were saying, but you weren't really listening because it was boring or it didn't make much sense.