Although the name could reference the crossbreed between a Cocker Spaniel and a Poodle, this version of the cockapoo is when a man engages in anal sex with a woman and she leaves his member covered in fecal matter.
Joe: Hey Manno, did you hear about what happened to Mike last week?
Manno: No Joe, What happened?
Joe: It's pretty disgusting, Mary was so wasted she cockapooed
Mike. I heard it took him five hours to wash it off.