Method for cutting out a section of a workpiece using a laser beam, and an associated laser cutting machine

The invention relates to a method for cutting out a section (2) of a workpiece from a planar workpiece (4), along a target course (3) and by means of a laser beam (5) of a laser cutting machine (1) that comprises a first drive (6) for moving the workpiece (4) at least along a first drive axis (X), and a second drive (7) for moving a laser cutting head (8), which aligns said laser beam (5) onto the workpiece (4), at least along the first drive axis (X). In said method, drive axis target values (XS) of the target course (3) of the laser beam (5) are divided into drive axis target values (XG) for the first drive (6) and drive axis target values (XF) for the second drive (7). According to the invention, with effect from a point in time lying around at least the braking time of the first drive (6) prior to the final cut-out position (F) of the workpiece section (2), the drive axis target values (XG) for the first drive (6) are converted to a constant drive axis target value such that once said first drive (6) brak