Hybrid additive and subtractive manufacturing is development in metal additive manufacturing techniques, wherein the dry cutting cooling method for subtractive cutting is one of the key technologies. To improve the milling performance of GH4169 alloy (namely Inconel 718 nickel-based superalloy) additive manufacturing parts, a dry cutting cooling method with a cryogenic gas jet and its effects on the cutting performance were investigated in this study. The theoretical model of the cryogenic gas jet flow was established, and the geometric characteristics, motion characteristics, and temperature distribution of the jet flow were analyzed. Meanwhile, considering the design of the nozzle outlet, the jet flow core length with a single nozzle and jet flow field envelope effect on the cooling heat transfer process with multiple nozzles were analyzed using a finite element simulation. Then, milling experiments on GH4169 alloy additive manufacturing parts with different cryogenic gas jet flow parameters were carried out. To reduce tool wear and the machined surface roughness of various parts, the jet flow parameters were optimized using the response surface analysis method. The effects of the milling feed direction on the tool wear and machined surface roughness were investigated. Furthermore, the tool wear morphologies were observed under different continuous milling times. The chemical compositions of the worn zone and tool wear mechanism were analyzed. The results show that cryogenic gas jet cooling can significantly improve the tool life and machined surface roughness of parts for GH4169 alloy additive-manufacturing-part milling, and the continuous cutting time within the tool wear allowance can reach approximately 50 min.