A wire saw apparatus 1 executes cut-machining by pressing a workpiece W against a cutting wire 3 spirally wound around multiple wire guides 2, while running the cutting wire 3 and simultaneously swinging the wire guides 2 as well as the cutting wire 3. The wire saw apparatus 1 includes a controller 8 controlling a position of a workpiece holder 51 for holding the workpiece W. The position is controlled depending on a swing angle of the cutting wire 3 so that machined portion of the workpiece W is shaped into an arc.