The method serves for operating a cutting device (1), which is intended for cutting a process material, in particular a food (8), and which has at least one blade (11), which is driven by a drive device (12) and to which ultrasonic energy is supplied from an ultrasound unit (4) by way of at least one energy converter (13) and a coupling element (15). The invention provides a control unit (6), which controls the ultrasound unit (4) in such a way that the frequency of the ultrasound energy supplied to the blade (11) by way of only one coupling element (15) is keyed between at least a first and a second operating frequency (f1a, f1b) or that the ultrasonic energy is supplied to the blade (11) at a first operating frequency (f1) by way of a first coupling element (15A) and at a second operating frequency (f2) by way of a second coupling element (15B), which frequencies are fixed or are keyed between at least two operating frequencies (f1, f2 or f1a, f1b; f2a, f2b).