A method for cutting a rare earth alloy of this invention includes cutting an object to be machined while supplying slurry containing dispersed abrasive grains between a wire and the object to be machined. The wire is driven with a drive member, at least a wire contact face of the drive member being composed of an organic polymer material. Cutting is carried out while a tension in a range between 14.7 N and 39.2 N is applied to the wire.