<p>An automatic cutting device for trimming off the parts (15) of an intermediate sheet (6) of plastics material which extend beyond a laminated pane (2) during manufacture. The device comprises a cutting head (1) provided with a blade (10) carried by a blade holder (23) which is heated by induction; means (11, 16) which hold the parts of the sheets of plastics material to be cut in a position at least substantially perpendicular to the plane containing the cutting edge of the blade (10); and means (9) causing relative displacement of the cutting head (1) along the edge of the pane (2).</p>