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In this study, the water-jet-guided laser (WJGL) method was used to cut Inconel 718 alloy with high temperature resistance. The effect of critical parameters of the water-jet-guided laser machining method on the cutting depth was studied by a Taguchi orthogonal experiment. Furthermore, the mathematical prediction model of cutting depth was established by the response surface method (RSM). The validation experiments showed that the mathematical model had a high predictive ability for cutting depth. The optimal cutting depth was obtained by model prediction, and the error was 5.5% compared with the experimental results. Compared with the traditional dry laser cutting, the water conducting laser method reduced the thermal damage and improved the cutting quality. This study provides a reference for the precision machining of Inconel 718 with a water-jet-guided laser.