The invention relates to a separation and recovery device and a method for argon and methane in synthetic ammonia relief gas, the separation and recovery device comprises a cold box, a raw material relief gas pipeline, a purification system which is communicated with the raw material relief gas pipeline and provided with a first molecular sieve adsorber MS1 and a second molecular sieve adsorber MS2, a refrigeration system for providing cold energy required for separating and liquefying, and a distillation system for separating raw material relief gas stage by stage, wherein the refrigeration system comprises a low-pressure circulation nitrogen compressor TC1, a medium-pressure circulation nitrogen compressor TC2, a low-temperature pressurized turbo-expander ET2, a high-temperature pressurized turbo-expander ET1, a main heat exchanger E1 and a liquefier E2, the distillation system comprises a flash evaporation tank S2, a dehydrogenation tower C1 equipped with a first condenser K4 and afirst evaporator K1, a dehydrogenation tower C2 equipped with a second condenser K5 and a second evaporator K2 and a product tower 3 equipped with a third condenser K6 and a third evaporator K3. The invention can obtain high product purify and high recovery rate.