A computer-controlled machining center, particularly a CAD/CAM cutting device for dental technology applications, includes a clamping device with a displaceably supported holding device on which a carrier plate for receiving a molded blank is supported. The carrier plate is formed with at least one passage opening to accommodate the molded blank pivotally about a pivot axis (a) that is substantially parallel to the main plane of the carrier plate. A clamping assembly allows the shaping blank to be mounted in the through opening rotatably about an axis of rotation (b) that extends parallel to the main plane of the carrier plate and encloses a given angle, preferably 90°, with the pivot axis (a) of the carrier plate.