This paper presents the simulation and design of an all-optical subtractor using a quantum-dot semiconductor optical amplifier Mach-Zehnder interferometer (QD-SOA MZI) structure consisting of two cascaded switches, the first of which produces the differential bit. Then the second switch produces the borrow bit by using the output of the first switch and the subtrahend data stream. Simulation results were obtained by solving the rate equations of the QD-SOA. The effects of QD-SOA length, peak power and current density have been investigated. The designed gate can operate at speeds of over 250 Gb/s. The simulation results demonstrate a high extinction ratio and a clear and wide-opening eye diagram.