Device for sharpening blades of cutting-off machines, comprising two grinding wheels (1) each positioned on a corresponding side of a cutting edge (20) of a blade (2) of a cutting machine. The device comprises means adapted for controlling the symmetry of said cutting edge (20), with a sensor (3) placed at a predetermined distance from a corresponding side of the cutting edge (20. The sensor (3) is adapted to detect possible differences (d) between the lengths (n, p) of the two sides of the cutting edge (20). The sensor (3) is connected to a programmable unit (4) that processes the said difference (d) possibly detected by the sensor (3).