A method cuts semiconductor wafers. The method includes: cutting a semiconductor ingot into a workpiece; and sawing the workpiece into slices using a wire grid having a fixed abrasive grain wire, while moving workpiece towards the wire grid. At a first contact of the workpiece with the wire grid, an initial cutting speed is less than 2 mm/min, coolant flow is less than 0.1 l/h and a wire speed is greater than 20 m/s. The workpiece is then guided through the wire grid until a first cutting depth is reached, and then the coolant flow is increased to at least 2000 l/h. The cutting speed is reduced to less than 70% of the initial cutting speed between the first contact of the workpiece with the wire grid up to a cutting depth of half a diameter of the cylinder, and is then increased.