deaf-mute vs deaf-and-dumb

deaf-mute is a noun but deaf-and-dumb is not a noun.

Word	Noun	Adjective	Verb	Adverb
deaf-mute	Yes	Yes	No	No
deaf-and-dumb	No	Yes	No	No

As adjectives, deaf-mute and deaf-and-dumb are synonyms defined as:

deaf-mute and deaf-and-dumb: lacking the sense of hearing and the ability to speak

deaf-mute (noun)	deaf-and-dumb (noun)
a deaf person who is unable to speak

deaf-mute (adjective)	deaf-and-dumb (adjective)
lacking the sense of hearing and the ability to speak	lacking the sense of hearing and the ability to speak