The invention relates to an apparatus for cutting a packaging material (4) for a package, comprising an ultrasonic welding device (2) that includes a sonotrode (3) and an anvil (5) for sealing the packaging material (4), the sonotrode (3) being rotatable about a first axis of rotation (X) and the anvil (5) being rotatable about a second axis of rotation (Y). The apparatus further comprises a cutting device (6) which includes at least one knife (7) for cutting the packaging material (4) and which is arranged within the anvil (5). The invention is characterized in that the knife (7) has a blade (8) with a cutting edge (28) that includes at least two tips (33, 35) and at least two curved sections (22) interconnecting the two tips (33, 35).