deaf mute 
dated or offensive Usage
noun
A person who is both deaf and unable to speak.In all, 57 Mexican deaf mutes were forced to labor from dawn to midnight, selling $1 trinkets on the subways and at New York's airports....
- Finally, to reduce rehearsal time, they added several new characters such as Louise, Dawn and Dinah who are all deaf mutes who commit suicide off stage.
- At the age of 16 he became, like his father, a teacher of elocution and instructor of deaf mutes.
adjective
(Of a person) both deaf and unable to speak.There are around 30 deaf mute people in our church....
- Council officials have threatened to make an elderly widow and her deaf mute brother homeless because of a debt they ‘inherited’ from their dead parents.
- Villasenor asks us to follow him into the mind and soul of Zach, who, when he first appears, is bicycling across America with a deaf mute boy.
Usage
In modern use deaf mute has acquired offensive connotations (implying, wrongly, that such people are without the capacity for communication). It should be avoided in favour of other terms such as profoundly deaf.