Process for cutting machining of a workpiece by means of a cutting beam guided by a cutting head and a working gas beam guided by the cutting head, comprising the following successive steps -: Moving of the cutting head and the workpiece relative to each other so that the cutting head is positioned at a cutting height above a workpiece surface of the workpiece, Cutting of a workpiece part out of the workpiece thus leaving a residual workpiece, wherein the cutting beam is guided along the cutting contour of the workpiece part and the workpiece part is completely separated from the residual workpiece in a cut-out point of the cutting contour, wherein the working gas beam is directed on the workpiece surface and deflected by the workpiece surface, wherein by the working gas beam directed on the workpiece surface within a gas pressure zone a positive gas pressure acts on the workpiece and by the working gas beam deflected by the workpiece surface within a gas suction zone a negative pressure acts on the workpiece, Turning off the cutting beam Moving the cutting head and the workpiece relative to each other, such that a) in a first movement phase without an enlargement of a vertical distance between the cutting head and the workpiece surface as given by the cutting height the cut-out point is positioned in the gas suction zone, wherein the cutting head in the first movement phase, starting from the cut-out point, is moved into the direction of the residual workpiece, wherein the relative movement between the cutting head and the workpiece is ended in the first movement phase if the cut-out point is located within a working region of the gas suction zone in which the negative gas pressure differs by a maximum of 50% from a minimum negative gas pressure of the gas suction zone, and b) in a second movement phase subsequent to the first movement phase, the vertical distance between the cutting head and the workpiece surface is increased. Moving of the cutting head and the workpiece relative to each other so that the cutting head is positioned at a cutting height above a workpiece surface of the workpiece, Cutting of a workpiece part out of the workpiece thus leaving a residual workpiece, wherein the cutting beam is guided along the cutting contour of the workpiece part and the workpiece part is completely separated from the residual workpiece in a cut-out point of the cutting contour, wherein the working gas beam is directed on the workpiece surface and deflected by the workpiece surface, wherein by the working gas beam directed on the workpiece surface within a gas pressure zone a positive gas pressure acts on the workpiece and by the working gas beam deflected by the workpiece surface within a gas suction zone a negative pressure acts on the workpiece, Turning off the cutting beam Moving the cutting head and the workpiece relative to each other, such that a) in a first movement phase without an enlargement of a vertical distance between the cutting head and the workpiece surface as given by the cutting height the cut-out point is positioned in the gas suction zone, wherein the cutting head in the first movement phase, starting from the cut-out point, is moved into the direction of the residual workpiece, wherein the relative movement between the cutting head and the workpiece is ended in the first movement phase if the cut-out point is located within a working region of the gas suction zone in which the negative gas pressure differs by a maximum of 50% from a minimum negative gas pressure of the gas suction zone, and b) in a second movement phase subsequent to the first movement phase, the vertical distance between the cutting head and the workpiece surface is increased. a) in a first movement phase without an enlargement of a vertical distance between the cutting head and the workpiece surface as given by the cutting height the cut-out point is positioned in the gas suction zone, wherein the cutting head in the first movement phase, starting from the cut-out point, is moved into the direction of the residual workpiece, wherein the relative movement between the cutting head and the workpiece is ended in the first movement phase if the cut-out point is located within a working region of the gas suction zone in which the negative gas pressure differs by a maximum of 50% from a minimum negative gas pressure of the gas suction zone, and b) in a second movement phase subsequent to the first movement phase, the vertical distance between the cutting head and the workpiece surface is increased.