Saw cords made of saw beads threaded on a steel cord, where the saw beads are separated by polymer spacers. The saw beads have a metal sleeve of which the outer surface is covered with an abrasive layer. The inner surface of the sleeve has with two sets of parallel grooves in a first and second axial part of the sleeve. The two sets of parallel grooves differ in at least one of the groove angle, the groove offset or the groove spacing, thereby preventing axial movement of the sleeve and blocking the rotation of the saw bead.