Machine for performing cutting operations on laminated glass plates, comprising: - a workbench, defining a supporting plane which is to receive the plate to be worked, - a fixed cutting bridge on which an upper carriage, carrying an upper incision tool, and a lower carriage, carrying a lower incision tool, are movably mounted in a direction Y parallel to the longitudinal direction of the cutting bridge, said cutting bridge being provided with actuating means for driving the movement of said carriages (9, 10) along the Y direction, - means for moving said plate on the fixed workbench in a horizontal direction X orthogonal to said Y direction, - means (12a, 12b, 14, 15) for causing the plate, or a plate portion cut by said cutting bridge, to rotate on said supporting plane, said rotating means comprising: - a gripping member for gripping a rear edge of the plate (with reference to the direction of advancement of the plate on the supporting plane), and at least one plate engagement member (14, 15) adapted to engage said rear edge of the plate at a point spaced apart from said gripping member, - said gripping member and said engagement member (14, 15) being respectively movable along the Y direction of the cutting bridge and along the X direction of the plate supporting plane, and - said machine further comprising an electronic control unit configured to drive a synchronous movement of said gripping member and said engagement member (14, 15) respectively along the Y direction and the X direction to obtain a rotation of the plate on the supporting plane, and - wherein said gripping member comprises at least one suction-cup element configured to engage one face of the plate adjacent to said rear edge, said suction-cup element being supported so that it is freely rotatable around a vertical axis by one of said carriages (9,10) and being movable by actuating means along said vertical axis between a position for engaging the plate and a positions spaced apart from the plate, characterized in that said gripping member further comprises a second element cooperating with said suction-cup element and configured to engage the face of the plate opposite to that engaged by the suction-cup element adjacent to said rear edge, said second cooperating element being carried by a respective carriage so that it is freely rotatable around a vertical axis coincident with the vertical axis of rotation of said suction-cup element and being movable by actuating means along said vertical axis between a position for engaging the plate and a position spaced apart from the plate, and in that said electronic control unit is programmed to control both said suction-cup element and said cooperating element, by activating only one or both these elements, depending upon the characteristics of the glass plate and/or the operative speed which is required. - a workbench, defining a supporting plane which is to receive the plate to be worked, - a fixed cutting bridge on which an upper carriage, carrying an upper incision tool, and a lower carriage, carrying a lower incision tool, are movably mounted in a direction Y parallel to the longitudinal direction of the cutting bridge, said cutting bridge being provided with actuating means for driving the movement of said carriages (9, 10) along the Y direction, - means for moving said plate on the fixed workbench in a horizontal direction X orthogonal to said Y direction, - means (12a, 12b, 14, 15) for causing the plate, or a plate portion cut by said cutting bridge, to rotate on said supporting plane, said rotating means comprising: - a gripping member for gripping a rear edge of the plate (with reference to the direction of advancement of the plate on the supporting plane), and at least one plate engagement member (14, 15) adapted to engage said rear edge of the plate at a point spaced apart from said gripping member, - said gripping member and said engagement member (14, 15) being respectively movable along the Y direction of the cutting bridge and along the X direction of the plate supporting plane, and - said machine further comprising an electronic control unit configured to drive a synchronous movement of said gripping member and said engagement member (14, 15) respectively along the Y direction and the X direction to obtain a rotation of the plate on the supporting plane, and - wherein said gripping member comprises at least one suction-cup element configured to engage one face of the plate adjacent to said rear edge, said suction-cup element being supported so that it is freely rotatable around a vertical axis by one of said carriages (9,10) and being movable by actuating means along said vertical axis between a position for engaging the plate and a positions spaced apart from the plate,