When you mutter, you mumble under your breath, often in an angry way. You might mutter to yourself as you clean graffiti off your garage, for example.
An irritable teenager might mutter when her parents make her get off the couch and mow the lawn, and your uncle might mutter at the television every night when he watches the news. When someone mutters, she speaks in a low voice, either to herself or to another person. Mutter was originally moteren in the fourteenth century, and it comes from a Proto-Indo-European root, mut, which was most likely imitative — in other words, it sounds like its meaning.