A pair of dies may be coupled to a machine for cutting threaded rods. The machine has a pair of arms each configured to hold one die. At least one arm is moveable relative to the other arm to cause the dies to shear a threaded rod. Each die includes a body having a front face, a rear face, a side face extending between the front face and the rear face, a cutting edge at a junction between the side face and the front face, and a threaded arcuate recess in the side face, configured to receive a threaded rod to be cut. The dies may be substantially identical so the dies can be reversibly attached in either of the arms. The threads of the arcuate recesses may form a continuous helical path about a threaded rod when the dies are closed around the threaded rod.