A sponge-like pad used for cleaning and other wiping and polishing applications is disclosed. The sponge-like pad is made from a plurality of textured paper webs attached together at selected locations. The paper web can be, for instance, a highly textured throughdried paper web containing high-yield fibers and a wet strength agent. In one embodiment, the stacked plies can be contained within a cover material that is liquid pervious. The sponge-like product of the present invention can be used alone or it can be incorporated into a cleaning tool, such as a mop.