The present invention pertains to a cutting machine for the automated cutting of at least one flat piece of deformable material. The machine comprises a cutting table which supports a cutting mat, a cutting unit provided with a blade and movable above the cutting mat to cut the flat piece into shapes and/or along lines according to a predetermined cutting path, an accessory processing unit provided with at least one accessory tool and movable over at least a portion of the cutting mat to perform accessory processing of the flat piece according to a predetermined accessory processing path, and an electronic control unit that controls the cutting unit and the accessory processing unit so as to actuate the accessory processing unit simultaneously to the cutting unit at least during a cutting step of the flat piece.