Machine for cutting sheets, particularly of marble, granite, glass and composite materials, comprising: - at least a base frame (2, 3); - at least a work top for at least a sheet to be cut, which is associated with said base frame (2, 3); - at least a cutting head, having at least a cutting tool to cut said sheet and associated with said base frame (2, 3) by interposition of first movement means (7, 8, 9) of said cutting head; - at least a gripping/retention head (13, 14) of said sheet, for grasping the sheet, or for holding it or for both grasping and holding it, associated with said base frame (2, 3) by interposition of second movement means (15, 16) of said gripping/retention head (13, 14), said second movement means (15, 16) being separate and independent from said first movement means (7, 8, 9) and comprising: - at least a first guide unit, associated with said base frame (2, 3) and suitable for moving said gripping/retention head (13, 14) along a first direction substantially parallel to said work top; and - at least a second guide unit, associated with said first guide unit sliding along said first direction and suitable for the movement of said gripping/retention head (13, 14) along a second direction substantially parallel to said work top and transversal to said first direction; characterized by the fact that it comprises at least two of said gripping/retention heads (13, 14), of which a first head and a second head, and by the fact that both said first head and said second head are associated with said second guide unit, said first head and said second head moving along said second guide unit independently the one from the other. - at least a base frame (2, 3); - at least a work top for at least a sheet to be cut, which is associated with said base frame (2, 3); - at least a cutting head, having at least a cutting tool to cut said sheet and associated with said base frame (2, 3) by interposition of first movement means (7, 8, 9) of said cutting head; - at least a gripping/retention head (13, 14) of said sheet, for grasping the sheet, or for holding it or for both grasping and holding it, associated with said base frame (2, 3) by interposition of second movement means (15, 16) of said gripping/retention head (13, 14), said second movement means (15, 16) being separate and independent from said first movement means (7, 8, 9) and comprising: - at least a first guide unit, associated with said base frame (2, 3) and suitable for moving said gripping/retention head (13, 14) along a first direction substantially parallel to said work top; and - at least a second guide unit, associated with said first guide unit sliding along said first direction and suitable for the movement of said gripping/retention head (13, 14) along a second direction substantially parallel to said work top and transversal to said first direction; - at least a first guide unit, associated with said base frame (2, 3) and suitable for moving said gripping/retention head (13, 14) along a first direction substantially parallel to said work top; and - at least a second guide unit, associated with said first guide unit sliding along said first direction and suitable for the movement of said gripping/retention head (13, 14) along a second direction substantially parallel to said work top and transversal to said first direction;