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) brakes, the workpiece section (2) is then only cut out by moving the laser cutting head (8), the workpiece (4) coming to a stop at the latest at the final cut-out position (F). The course division is implemented by means of a low pass filter (11) that filters the low-frequency drive axis target values (XG) out from the drive axis target values (XS) that have been fed in, and a subtractor (12) that determines the high-frequency drive axis target values (XF) in the form of a difference between the original drive axis target values (XS) and said low-frequency drive axis target values (XG). According to the invention, an actuatable switch (15) is connected upstream of said low pass filter (11) and, when in one of its switching positions, forwards on the fed-in drive axis target values (XS) and, when in its other switching position, forwards on a constant drive axis target value (XS
const ) to said low pass filter (11).