A method for laser cutting a workpiece, including generating a machining laser beam, for cutting the workpiece and for producing cuts with cut edges in the workpiece; generating at least two energy intensity ranges (15a, 15b, 15c) of the machining laser beam, characterized by splitting the machining laser beam into the at least two energy intensity ranges (15a, 15b, 15c) of which a first energy intensity range for cutting the workpiece has a greater time-integrated radiation energy than at least one second energy intensity range (15b, 15c) for at least partially refining and processing a cut edge, wherein - the first energy intensity range is generated as a core region of the machining laser beam for producing a cutting gap in a region and for separating the workpiece into two sheets, each having a cut edge, and the at least one second energy intensity range (15b, 15c) is generated as at least one edge region of the machining laser beam for refining and processing the surface structure of the cut edge, and - the first energy intensity range and the at least one second energy intensity range (15b, 15c) are arranged concentrically,; irradiating the workpiece with the machining laser beam, cutting of the workpiece with the first energy intensity range, thereby producing a cutting gap in a region and separating the workpiece into two sheets, each having the cut edge and at least partially refining and processing the cut edge of the workpiece with the at least one second energy intensity range (15b, 15c), thereby refining and processing the surface structure of the cut edge; wherein the energy intensity ranges (15a, 15b, 15c) of the machining laser beam are generated by means of dynamic beam shaping. including generating a machining laser beam, for cutting the workpiece and for producing cuts with cut edges in the workpiece; generating at least two energy intensity ranges (15a, 15b, 15c) of the machining laser beam, characterized by splitting the machining laser beam into the at least two energy intensity ranges (15a, 15b, 15c) of which a first energy intensity range for cutting the workpiece has a greater time-integrated radiation energy than at least one second energy intensity range (15b, 15c) for at least partially refining and processing a cut edge, wherein - the first energy intensity range is generated as a core region of the machining laser beam for producing a cutting gap in a region and for separating the workpiece into two sheets, each having a cut edge, and the at least one second energy intensity range (15b, 15c) is generated as at least one edge region of the machining laser beam for refining and processing the surface structure of the cut edge, and - the first energy intensity range and the at least one second energy intensity range (15b, 15c) are arranged concentrically,; - the first energy intensity range is generated as a core region of the machining laser beam for producing a cutting gap in a region and for separating the workpiece into two sheets, each having a cut edge, and the at least one second energy intensity range (15b, 15c) is generated as at least one edge region of the machining laser beam for refining and processing the surface structure of the cut edge, and - the first energy intensity range and the at least one second energy intensity range (15b, 15c) are arranged concentrically,; irradiating the workpiece with the machining laser beam, cutting of the workpiece with the first energy intensity range, thereby producing a cutting gap in a region and separating the workpiece into two sheets, each having the cut edge and at least partially refining and processing the cut edge of the workpiece with the at least one second energy intensity range (15b, 15c), thereby refining and processing the surface structure of the cut edge; wherein the energy intensity ranges (15a, 15b, 15c) of the machining laser beam are generated by means of dynamic beam shaping.