The invention concerns a grinding machine having displaceable grinding means for the processing of workpieces made from wood, wood composite materials, plastics, metals and similar materials. The invention further concerns a method of grinding a workpiece by means of the inventive grinding machine. The grinding aggregate comprises: at least one translational driving means configured to translate the grinding means (6) and at least one eccentric tappet configured to rotatingly move the grinding means (6). The inventive device is characterized in that the grinding aggregate comprises a suctioning device which suctions waste products of the processing, such as chips, through the grinding means. In this way, it is possible to achieve a qualitatively superior grinding result.