1901, "stupid or foolish person," probably a shortening of muttonhead (1803) in the same sense; see mutton and compare meathead, etc. Mutt was used by 1898 of a dog, especially a stupid one, and perhaps this is the same word formed independently (muttonhead also was used of stupid animals), or else a separate word of unknown derivation. Wright's "English Dialect Dictionary" (1900) has "Mutton! used in scolding a dog, prob. in allusion to the offence of sheep-worrying."
"That dog ain't no mutt," McManus would say as he stood behind the bar opening oysters; "no an he ain't no rube! Say! he's in it all the time when Charley trims the steaks." [Robert W. Chambers, "The Haunts of Men," 1898]
Used by 1910 in dog fancier publications to refer to a non-purebred animal.