A cutter device for cutting road markings on a road surface, the cutter device including a frame for suspending a cutter unit from a road traffic vehicle, a cutter unit connected to the frame, and support equipment for supporting the cutter unit to the frame movably in the vertical direction, said cutter unit comprising - a cutter frame, - a rotating cutter blade mounted with bearings to the cutter frame for cutting a road marking on a road surface, and - a support wheel connected to the cutter frame for supporting the cutter unit against a road surface, wherein the cutter device additionally includes - height adjustment equipment arranged in the vicinity of the cutter frame for moving the cutter frame in the vertical direction relative to the frame and the road surface for adjusting the cutting depth of the cutter blade, - pressing equipment arranged in the vicinity of the cutter frame between the cutter frame and the frame or the cutter frame and the road traffic vehicle for pressing the cutter blade against the road surface during the cutting process, - side-shift equipment for moving the cutter unit transversely to the road traffic vehicle below the road traffic vehicle between the operating position and the storage position, characterised in that the cutter device further includes - suction equipment arranged at least partially in the vicinity of said cutter unit for sucking road surface material produced detaching during the cutting process from the road surface, - traction equipment for delivering traction with the support wheel for rotating the support wheel substantially at a speed corresponding to the travel speed of the road traffic vehicle to which the cutter device is to be suspended, and said support wheel is asymmetric for supporting the cutter unit against an uncut surface of the road in such a way that the rotating cutter blade contacts the road surface periodically while a profile of the support wheel follows the road surface for cutting repeated road markings on the road surface. - a cutter frame, - a rotating cutter blade mounted with bearings to the cutter frame for cutting a road marking on a road surface, and - a support wheel connected to the cutter frame for supporting the cutter unit against a road surface, wherein the cutter device additionally includes - height adjustment equipment arranged in the vicinity of the cutter frame for moving the cutter frame in the vertical direction relative to the frame and the road surface for adjusting the cutting depth of the cutter blade, - pressing equipment arranged in the vicinity of the cutter frame between the cutter frame and the frame or the cutter frame and the road traffic vehicle for pressing the cutter blade against the road surface during the cutting process, - side-shift equipment for moving the cutter unit transversely to the road traffic vehicle below the road traffic vehicle between the operating position and the storage position, characterised in that the cutter device further includes - suction equipment arranged at least partially in the vicinity of said cutter unit for sucking road surface material produced detaching during the cutting process from the road surface, - traction equipment for delivering traction with the support wheel for rotating the support wheel substantially at a speed corresponding to the travel speed of the road traffic vehicle to which the cutter device is to be suspended,