A device for monitoring, in particular for regulating, a cutting process on a workpiece, comprising: a focusing element for focusing a high-energy beam, in particular a laser beam, onto the workpiece, an image capture apparatus for capturing a region at the workpiece to be monitored, said region comprising an interaction region of the high-energy beam with the workpiece, and an evaluation apparatus embodied to determine at least one characteristic variable (α) of the cutting process, in particular of a kerf formed during the cutting process, on the basis of the captured interaction region, wherein the image capture apparatus is embodied to form an observation beam for observing the interaction region from an observation direction extending at an angle (β) to the beam axis of the high-energy beam and wherein the image capture apparatus comprises an imaging optics for generating an image of the interaction region from the observation direction extending at the angle (β) to the beam axis of the high-energy beam, and a detector, in particular a camera, with a detector surface, at which the image is generated, characterized in that the imaging optics is embodied to image, on the detector surface, the observation beam which extends eccentrically to the central axis of the focusing element and thus extends in the convergent beam path between the focusing element and the workpiece at the angle (β) to the beam axis of the high-energy beam, wherein the device comprises a control apparatus which is embodied to modify the alignment of the observation direction (R1, R2,...) in a projection in a plane (X, Y) perpendicular to the beam axis in a manner dependent on an advance direction (v) of the cutting process. a focusing element for focusing a high-energy beam, in particular a laser beam, onto the workpiece, an image capture apparatus for capturing a region at the workpiece to be monitored, said region comprising an interaction region of the high-energy beam with the workpiece, and an evaluation apparatus embodied to determine at least one characteristic variable (α) of the cutting process, in particular of a kerf formed during the cutting process, on the basis of the captured interaction region, wherein the image capture apparatus is embodied to form an observation beam for observing the interaction region from an observation direction extending at an angle (β) to the beam axis of the high-energy beam and wherein the image capture apparatus comprises an imaging optics for generating an image of the interaction region from the observation direction extending at the angle (β) to the beam axis of the high-energy beam, and a detector, in particular a camera, with a detector surface, at which the image is generated, characterized in that the imaging optics is embodied to image, on the detector surface, the observation beam which extends eccentrically to the central axis of the focusing element and thus extends in the convergent beam path between the focusing element and the workpiece at the angle (β) to the beam axis of the high-energy beam, wherein the device comprises a control apparatus which is embodied to modify the alignment of the observation direction (R1, R2,...) in a projection in a plane (X, Y) perpendicular to the beam axis in a manner dependent on an advance direction (v) of the cutting process.