The invention relates to a cutting device and method for cutting prefabricated transverse seal seams of a tube composed of plastic film and filled with food, particularly soft cheese, wherein each transverse seal seam of the continuously supplied film tube to be processed separates one portion of the food from the next portion. The device comprises a rotating knife holder provided with at least one knife blade 22, and wherein the knife blade 22 acts on a counter bearing 4 when cutting a transverse seal seam, wherein said knife holder has a heating element for heating the knife blade 22 in a targeted fashion.