Yes, some people are mute because they are born deaf, or become deaf in their early childhood, but even most deaf people can and do make sounds, including speech.

Other people, who do not have any hearing problems may be mute due to a whole host of problems including extreme social anxiety, physical problems with their throat or mouths, or vocal chords, neurological problems, mental or social problems such as autism or extreme retardation, or conditions such as post traumatic stress disorder, even though they have the physical potential to be able to speak. You can read more about these causes under Selective Mutism

Being Mute is seperate from deafness, though sometimes someone has both problems.