The invention relates to a cutting device for a granulator for obtaining granules from cutting plastic strands which are discharged from nozzles, said cutting device comprising a cutting rotor which is connected to the drive shaft by means of a Cardan joint piece comprising a driven part and a drive part. Said drive part and the driven part comprise a force transfer piece, respectively having a prong like shape such that the prongs rotate about the force transfer piece when they are pivoted at about 90 degrees in relation to each other. Each prong supports the axis which extends through the force transfer piece and both axes are offset in relation to each other essentially about 90 degrees.