Abstract: A chamfer cutting device for cuffing packaging materials comprises a die and a knife part which has a plurality of knives. The die can be moved toward the knife part in order to carry out a cut. The knives are arranged individually in the knife part in a force-dependent manner in such a way that their position with respect to the tool plate varies in a defined way as a function of the force produced by contact with the packaging material or the die. In the event of contact between the knife and the die, a force acts on the knife which does not exceed a predefined maximum force. The chamfer cutting device has the advantage that the die can be guided right up to the knives.