The invention relates to a finishing device for removing the weld bead generated during welding of a window or door frame or frame section at the mitered surfaces, wherein the finishing device comprises a support surface for the frame or frame section and a processing arm for supporting a tool holder, and the processing arm consists of a plurality of arm elements that move in hinged fashion relative to one another but can also be fixed in place, wherein the tool holder comprises at least two cutting tools driven by a rotational drive, said tools rotating about a tool axis and at least one tool laterally next to the blade of the tool, contact sides.