A device for cutting material on a supporting surface has at least one cutting unit, which can be motor-driven in a controlled manner above and across the supporting surface in a direction of an X- and Y-axis of a Cartesian coordinate system that is parallel to the material supporting surface. The at least one cutting unit comprises an oscillation drive and a cutting knife. The oscillation drive sets the cutting knife into linear oscillations having an oscillation axis that is perpendicular to an advancing direction of the cutting knife. For changing an angle of inclination of the oscillation axis with respect to the material supporting surface, the oscillation drive with the cutting knife is pivotable around a pivot axis that is parallel to the material supporting surface. The oscillation drive comprises an electric motor having a rotary drive shaft that is parallel to the material supporting surface. The rotary axis of the rotary drive shaft is aligned with the pivot axis.

A device for the cutting of material on a plane material supporting surface, the device having at least one cutting unit which can be motor-driven in a controlled manner above the material supporting surface in the direction of the X- and Y-axis of a Cartesian coordinate system that is parallel to the material supporting surface, and having an oscillation drive and a cutting knife, wherein the oscillation drive sets the cutting knife into linear oscillations along an oscillation axis that is perpendicular to the advancing direction of the cutting knife. The cutting knife is pivotable around a pivot axis that is parallel to the material supporting surface and is aligned with the rotary axis of a rotary drive shaft of an electric motor of the oscillation drive.