Mutius is one of Titus's sons. Although he survives Rome's long war with the Goths, he's killed (by his own father!) on the day of his return home, when he tries to help Bassianus run off with Lavinia.
Mutius isn't a major character in the play, but his death is important because it suggests to us that parents can't always be trusted to care for their children. This becomes even more obvious as the play continues – Tamora involves her sons in her revenge plot by encouraging them to rape Lavinia, and Titus will later kill his only daughter.