deaf-and-dumb vs deaf-mute

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

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

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

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

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

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