A deaf-mute is someone who cannot hear or speak. This word could cause offence.
deaf-mute in British English
old-fashioned, offensive
noun
1.
a person who is unable to hear or speak
See also mute1 (sense 7), mutism (sense 2b)
adjective
2.
unable to hear or speak
▶ USAGE Using this word to refer to people without speech is considered outdated and offensive,and should be avoided. The phrase profoundly deaf is a suitable alternative in many contexts
Derived forms
deaf-muteness (ˈdeaf-ˌmuteness) or deaf-mutism (ˈdeaf-ˌmutism)
noun
Word origin
C19: translation of French sourd-muet
deaf-mute in American English
(ˈdɛfˌmjut)
noun
1.
a person who is deaf, esp. from birth, and therefore unable to speak: most deaf-mutes, having the necessary vocal organs, can be taught to speak