sleep off
To reduce or rid oneself of some unpleasant condition by getting extra sleep. A noun or pronoun can be used between "sleep" and "off." He drank a bit too much, but he'll be fine—he just needs to sleep it off. I think I'll head home early and try to sleep off this head cold.
sleep something off
to sleep while the effects of liquor or drugs pass away. John drank too much and went home to sleep it off. Bill is at home sleeping off the effects of the drug they gave him.
sleep off
v. To get rid of something while sleeping: She went home to sleep off her headache. He has a hangover—let him sleep it off.
sleep it off
tv. to sleep while the effects of drugs or alcohol wear off. I’m polluted, I guesh. Have to get home and sleep it off.