Disclosed herein is a machine for cutting nozzles of reactor vessels. The machine for cutting nozzles of reactor vessels comprises a cutting unit positioned at an upper surface edge of a reactor vessel having a nozzle and having a saw blade part having different contact areas to cut the nozzle, a drive unit providing the saw blade part with rotary power, and a foreign substance suction unit provided at one end of the cutting unit in contiguity with the saw blade part to suck foreign substances generated when the nozzle is cut by the saw blade part, wherein the foreign substance suction unit sucks the foreign substances by approaching an outer peripheral surface of the nozzle when the saw blade part moves in a cutting direction of the nozzle.