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.
Mutt and Jeff is by 1917 in reference to "a pair of stupid men, affable losers," or to one tall (Mutt) and one short (Jeff), from the comic strip characters from the heyday of the newspaper funny pages, Augustus Mutt and Jim Jeffries, in U.S. cartoonist Henry Conway ("Bud") Fisher's strip, which debuted in 1907.