Abrasive Water Jet Machining (AWJM) is a popular machining method used to machine polymer matrix composites that are sensitive to temperature. This method is non-thermal, and each input parameter has a significant effect on output parameters, such as material removal rate, kerf width, surface roughness, and the potential for delamination. To ensure high-quality machining, it is crucial to set these input parameters at their optimal level. This paper proposes a simple approach to predict the optimum process parameters of water jet machining operations on jute fiber-reinforced polymer composite (JFRPC). The process parameters considered are standoff distance (SOD), traverse speed (TS), and abrasive material flow rate (MFR). Conversely, surface roughness (Ra) and delamination (Da) are the output parameters. Process parameters are set using Taguchi’s L27 array, with consideration given to three levels of each input parameter. The best value for process parameters is found using grey relational analysis (GRA), and an ANOVA on GRA illustrates the impact of each input variable. After a confirmation test, it was found that the suggested parameters guarantee the best possible results.