A glass sheet (2) having two side glass sheets (3,4) and an intermediate sheet (5) of thermoplastic material is cut by a cutting machine (1) provided with an etching and breaking device (6,8) to divide the laminated glass sheet (2) into two pieces of sheet joined to each other by means of an elongated intermediate portion (12) of the thermoplastic material sheet (5), and a heating assembly (13) of the elongated intermediate portion (12); the heating assembly (13) being provided with an elongated source (15), adapted to emit a divergent heating beam having an optical axis (20) thereof intersecting the elongated intermediate portion (12), and a focusing assembly (22) for focusing at least part of the heating beam along at least a first elongated focusing line (24) either external to or intersecting the elongated intermediate portion (12) of the sheet of thermoplastic material.