Automatic-cycle machine for the cross-cutting of marble and granite strips with multiple diamond disks. Crosswise conveyance of strips on main conveyor where they are aligned at right-angles to the cutting line. The strips are held in position during the cutting by a set of automatically controlled presser rollers. Cutting with the possibility of excluding each single disk. Suction pad at tiles outfeed which lifts the tiles and places them on the conveyor belt.