A mop assembly includes a handgrip structure disposed above, connected telescopically to a rotary rod structure from above and a cleaning mop connected pivotally to a bottom end of the rotary rod structure. Once the cleaning mop is placed within a draining bucket, axially downward and upward movement of the handgrip structure relative to the rotary rod structure results in axial rotation of the rotary rod structure and the draining bucket relative to the handgrip structure in a predetermined direction and hence draining the water out from the cleaning mop.