A cutting machine comprises a workpiece changer possessing a receiving element for the workpieces and/or workpiece palettes, said receiving element being able to be pivoted about a vertical axis and to be linearly shifted in a plane normal to such axis. At least one slide arrangement is able to be power driven in the two horizontal directions for a tool spindle and is adapted to run on two parallel side walls of the cutting machine designed in the form of a gantry machine. The intermediate space between the side walls is divided by a transverse wall or by door, which during workpiece machining is closed and during the workpiece changing operation is at least partly open, into a front machining area and a rear supply area, the radius of pivoting of the receiving element, engaging a workpiece or a workpiece palette, extending at least partly into a supply area. Accordingly a person minding or controlling the functioning cutting machine is not hampered by workpiece changing.