Device for cutting a corneal epithelial cover includes a fixing ring (1), a suction source (4), a cutting head (5) which is movably mounted on the ring (1) and an oscillating blade (10), elements (7, 8) for actuating the cutting head movements with respect to the ring and elements for controlling a suction, the blade oscillation and actuation adjustment according to: a starting phase of the corneal cover cutting, wherein the suction level is maximum, the advancing speed of the head is minimum and the oscillation frequency of the blade is maximum, a phase for cutting the larger part of the corneal cover, wherein the advancing speed is maintained or increased and the oscillation speed and the suction level are maintained or reduced and a third phase, wherein the head speed is inverted, oscillations are stopped and the suction level is maintained at the reduced level of the second phase.