The innovative process of curved profile extrusion facilitates the cost-effective production of lightweight structures with spatially curved profiles even for small series. Due to the extrusion process a continuous flow of material is unavoidable. The profiles have to be separated reactionlessly during the extrusion following the complex trajectory of the cut-off point in space. This paper discusses the challenges for a flying cut-off device. In addition to a concept to generate the trajectories and control the movements, the main parameters for dimensioning a cut-off device are presented. A specially designed clamping device permits to generate high accelerations. Further on, cutting results are shown especially for extruded sections with continuous reinforcing elements of steel.