In a self-propelled construction machine or mining machine, in particular milling machine for working a ground surface, including a machine frame, a working device for working the ground surface, which is supported on the machine frame, wherein the working device is at least partially enclosed by a housing, at least one movable side plate, which closes the housing on at least one of the two sides of the working device , wherein the movable side plate rests on the ground surface in floating position during the working operation, it is provided that a clearing scraper is arranged in front of the at least one movable side plate as seen in the direction of travel, wherein the clearing scraper comprises at least one clearing edge for penetrating ground material lying on the ground surface in front of the movable side plate, and clears the ground material for the movable side plate so that the movable side plate may rest on the ground surface.