First and second dies can be coupled to a pair of arms on a threaded rod cutting machine. The first die has a body with a front face, a rear face, a side face extending between the front face and the rear face, and a first threaded recess in the first side face and configured to receive a threaded rod to be cut. Crests and troughs of the first thread are aligned with troughs and crests of the threaded rod when the first die engages the rod. The second die has a body with a front face, a side face extending between the front face and the rear face, and a second threaded recess in the side face and configured to receive the threaded rod. Crests and troughs of the second thread are axially offset from troughs and crests of the threaded rod when the second die engages the rod.