The invention relates to a device (1) for cutting wafers (2) into a number of chips with a laser beam (6) injected into a liquid jet (7). A thin flowing liquid layer (9) having a blasting effect is produced on the surface (5) of the wafer (2). This makes it possible to prevent projections resulting during laser cutting from depositing once again on the surface of the wafer. The result is a very high cleanness of the surface after the cutting process. The liquid layer (9) is produced, in particular, so that it is thinner in a machining area (10) around the machining point (8) than outside of the machining area (10). This ensures that the liquid layer is sufficiently thin (14) at the machining point (8) so that enough laser energy for removing material is applied to the wafer surface, and ensures that the liquid layer is sufficiently thick (15) outside of the machining area so that no area of the surface (5) of the wafer (2) dries out.