Madame L was thinking of this expression recently because it's one her dad used to say. Mutt and Jeff were comic strip characters created by cartoonist Harry "Bud" Fisher, according to the A.Word.A.Day website.
Mutt is tall and Jeff is short, and they're both "lovable losers." Nowadays when we use the term "Mutt and Jeff," we can be talking about any pair of comically mismatched characters. One could be tall and the other short, or one could be like Jack Spratt and the other like his wife, or one could be a chihuahua and the other a Saint Bernard.
The Word a Day website also notes that the expression, pronounced "mut uhn jef," is the word for "deaf" in Cockney rhyming slang.