A cutting machine having a workpiece changer possessing a receiving element for the workpieces and/or workpiece palettes, said receiving element pivots about a vertical axis and is linearly shiftable in a plane normal to such axis. A tool spindle moves on two parallel side walls which are divided by a transverse wall or by door which can opened or shut between a front machining area and a rear supply area. The radius of the receiving element extends at least partly into a supply area and the tool spindle is movable over the front machining area. Accordingly a person minding or controlling the functioning cutting machine is not hampered by workpiece changing.