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

This disclosure relates to methods and apparatuses for cutting out a workpiece section along a target path from a plate-shaped workpiece using a laser beam of a laser cutting machine having a first drive for moving the workpiece along a first drive axis, a second drive for moving a laser cutting head along the first drive axis. Target values of the target path of the laser beam are divided into target values for the first drive and for the second drive. Before the laser beam reaches a cutting-out end position of the workpiece section, the target values for the first drive are set to a constant value, so that after braking of the first drive, the cutting out of the workpiece section is only still executed by moving the laser cutting head and the workpiece comes to a stop at latest at the cutting-out end position.