In a method and a device for cutting freeform surfaces, a workpiece is cut by a tool or a cutter to produce a desired freeform surface. For the purpose of cutting, the tool is moved along at least one defined tool path or cutting path relative to the workpiece. In addition to the, or each tool path, at least one guide curve is defined for a tool vector of the tool, the tool vector being oriented as a function of the, or each guide curve 12 during the cutting.