Old English deaf "deaf," also "empty, barren," specialized from Proto-Germanic *daubaz (cf. Old Saxon dof, Old Norse daufr, Old Frisian daf, Dutch doof "deaf," German taub, Gothic daufs "deaf, insensate"), from PIE dheubh-, which was used to form words meaning "confusion, stupefaction, dizziness" (cf. Greek typhlos "blind).
The word was pronounced to rhyme with reef until 18c. Deaf-mute is from 1837, after French sourd-muet. Deaf-mutes were sought after in 18c.-19c. Britain as fortune-tellers. Deaf as an adder (Old English) is from Psalms lviii:5.