A cleaning mop has a cylindrical roller formed of adjacent disk-shaped rings of resilient foam material which engages and rotates relative to a floor surface to be cleaned to scrub the surface when the mop is pushed in a forward direction and picks up particles of debris when the mop is moved in either direction. When the mop is pushed in a forward direction; the roller is engaged by a drive mechanism to rotate; a valve opens and cleaning liquid flows onto the roller from an onboard reservoir and a gap is formed between the rings by separator fingers as they approach the floor surface; the roller rings engage and move relative to the floor surface and the gap closes to capture particles of debris between the rings; and the dirty liquid and particles carried around the circumferential path on the roller are removed by a squeegee plate and collected in an onboard collection tank. When the mop is pulled in the rearward direction, the roller is disengaged from the drive mechanism to rotate freely and the valve closes to shut off the supply of cleaning liquid. As the disengaged roller rolls on the floor surface the separator fingers widen the gap between the rings and as they approach and engage the floor surface the gap closes to capture particles of debris between the rings; and the particles carried around the circumferential path on the roller are removed by the squeegee plate and collected in the onboard collection tank.