A cutting device configured to be associated with a self-propelled mower, wherein the cutting device comprises a cutting member that comprises a plurality of oscillating blades to mow grass fixed to a support shaft, rotating with an axis of rotation that is horizontal and orthogonal to a direction of advance of the mower, a system for conveying the cut grass that comprises an auger, with axis of rotation parallel to the axis of rotation of the support shaft, and provided with at least one access opening for feeding the cut grass, from the oscillating blades, to the auger and at least one outlet for the exit of the cut grass, wherein the system for conveying cut grass comprises a grass accelerator positioned facing the outlet for the exit of the cut grass.
