Green’s has it from 1930, reporting a conversation had in 1917, so it likely dates to the earlier war:
1930 [US] (con. 1917) ‘W.W. Windstaff’ ‘A Flier’s War’ in Longstreet Canvas Falcons (1970) 280: H.Q. is chewing out my arse why we’re not flying right now.
1943 [US] Moss Hart Winged Victory I x: He just chews your can off.
1944 [US] N. Mailer letter 30 Apr. in Selected Letters (2014) 17: When you are bawled out by a sergeant or officer [...] it is called ‘getting your ass chewed out’.
The ass is dropped for propriety’s sake. Just imagine dogs, or some other predator, chasing you and taking bites out. The metaphor is pretty clear.