Piece Out

piece out refers to kicking out a "hookup" or "trick" from the night before. A "hookup" or "trick" is also referred to as a piece of meat...hence piece out.

The act of leaving a situation or a scenario dramatically with your fingers in the shape of guns pointed in the air, or blasting away imaginary bullets at others around you.

ALTERNATELY:

your piece may refer to a glass smoking pipe.