Green’s Dictionary of Slang

mouth-breather n.

[such individuals are presumed to be breathing heavily]

a stupid person, esp. a particularly stupid thug.

[US]S. Ford Torchy, Private Sec. 130: ‘You noticed her, didn’t you, Torchy?’ ‘The mouth breather? [...] That’s Ruby. Nobody home, and the front door left open.’.
[US]W. Wilson LBJ Brigade (1967) 39: He’s the king of the Mouth-breathers, all these yahoos leaning against walls with their mouths open and hands out.
[US]P. Munro Sl. U. 133: Will all the mouthbreathers leave so that we can get some work done?
skb’s virtual cave [Internet] Knuckle-draggers and mouth-breathers: John Birch Society ’Nuff said.
T. Shary Generation Multiplex 2: He’s a mouth breather, a guy you pray will remember to swallow so he doesn’t drool over his experiments.
[Aus]G. Disher Heat [ebook] Christ, he was a mouth-breather to boot. Didn’t he have the least bit of self-awareness?

In derivatives

mouth-breathing (adj.)

stupid, often stupid and thuggish.

[US]time 30 May 70: Vaclav Havel was talking about the mouth-breathing heavies who ran Czechoslovakia during the communist years [HDAS].
S. Wilcox Niagara Falls 88: Along comes a knuckle dragging, mouth breathing, garlic sucking Sicilian meatball of a Yank mafioso.
H. Chislett From This Place And Time 50: Who could say what provoked this knuckle-dragging, mouth breathing troglodyte to unleash his brain stemmed ire at me?