Green’s Dictionary of Slang

1. (US tramp) to wander around.

1915

Day Book (Chicago) 18 Mar. 14/1: Before it’s time to bum my next feed I’ll take a mope around and ‘shoot a snipe’ or two.

2. (US) to leave.

1926		Maines & Grant Wise-crack Dict. 6/2: Cop a mope – Take a walk.
1933		J. Spenser Limey 70: You’ll be gettin’ all the company ya want, I guess, so I’ll cop a mope.
1950		Goldin et al. DAUL 49/2: Cop a mope. [...] 2. To walk away; to leave.

3. (US prison) to escape.

1931		G. Milburn ‘Convicts’ Jargon’ in AS VI:6 437: cop a mope, v. To make an escape.
1936		L. Duncan Over the Wall 329: How would you like to take a mope, or have you got that stuff out of your bean?
1976		E. Thompson Caldo Largo (1980) 85: Hey, Pete, come on, let’s cop a mope.

4. (US) to hold back, to refrain from talking.

1974

(con. late 1940s) E. Thompson Tattoo (1977) 670: He would become like his uncle, who had never ‘conversed’ in his life. ‘Cop a mope,’ was how Jack’s stepfather would have put it.