The invention concerns a device for cutting a graft on a graft-slip, said device comprising a blade (15) and a support plate (7) for the graft slip, the blade being contained in a cutting plane, the support plate forming a longitudinal cutting angle with said cutting plane. Since the cutting angle results from a rotation centred on the cutting edge (16) of the blade, the device comprises a member for moving (17) the blade along a cutting plane towards the support plate.