The invention belongs to the technical field of argon recovery, and particularly relates to an argon recovery device for removing carbon monoxide through a rectification method and an operation method. The argon recovery device comprises an argon compressor, a deoxidizing reaction furnace, a cooler, an argon precooling and purifying system, and a rectification cold box; and a heat exchanger, an argon tower reboiler, a pure argon tower, a crude liquid argon throttle valve V2, a pure liquid argon throttle valve, a circulating liquid argon throttle valve V5 and an argon tower condensation evaporator are mounted in the rectification cold box. The device has the advantages that liquid argon can be conveniently provided by recycling the liquid argon in the field, and the liquid argon is used for providing cooling capacity; the mixed oxygen is removed by using hydrogen produced by water electrolysis hydrogen production, and nitrogen, carbon monoxide and excess hydrogen are removed by using the low-temperature rectification method, such that the greatest advantage is that a carbon monoxide removing device is omitted, the tolerance of raw material gas to the oxygen content is substantially improved, the argon gas recovery rate is improved, the low-temperature rectification process and operation are simplified, and the operation energy consumption is reduced.