PURPOSE: To efficiently manufacture a cutting wire having a helical groove or a discontinuous peripheral groove, by feeding a strand wire, while it is given predetermined tension, running continuously or intermittently in a predetermined speed and rotating a groove cutting tool while it is brought into contact with the strand wire.

CONSTITUTION: A strand wire S, fed from a bobbin 1 by a motor 2, is given predetermined tension between pulleys 3, 4 passing through a window 9a of a groove cutting part supporting bed 9, and the wire S, being guided by a wire guide block 16, comes into contact with a groove cutting tool 10. The groove cutting tool 10 is rotated by a motor 12, and if the supporting bed 9 is turned by a motor 26 through a turning table 8, the running wire S, which is cut forming a helical groove in the peripheral surface and changing into a cutting wire W, is wound on to a winding bobbin 5 by a motor 6 in the predetermined tension. The strand wire S, if it is driven running intermittently by intermittently driving the motors 2, 6, enables a discontinuous peripheral groove to be formed on surfaces of the wire W. Thus, the cutting wire can be efficiently manufactured.