Green’s Dictionary of Slang

(orig. US) a deaf mute.

1943		W. Guthrie Bound for Glory (1969) 284: What’s wrong? Bunchah dam dumb-dumbs? Can’t none of yu men say nuthin’?
1959		W. Brown Teen-Age Mafia 29: Everybody [was cozy] except Dum Dum [...] Because what frill would want a stud who couldn’t talk.
1969		L. Sanders Anderson Tapes 133: Two are drivers, one of them a dumdum [HDAS].