GLARE is a type of laminate material made up of layers of aluminum and fiberglass used in automotive, and aircraft structures like fuselage panels, control surfaces, and wing skins due to their superior specific strength, fatigue, and damage tolerance. The inclusion of nanoclay filler was reported to improve the mechanical properties of the GLARE laminates. However, it is important to investigate the machinability of such laminates to extend their applicability in the industry. The current work optimizes the process parameters of the Abrasive Water Jet Machining (AWJM) process to cut the nanoclay-modified Fiber Metal Laminates (FMLs). The experiments were designed by following Taguchi’s L9 orthogonal array. The influence of factors like the velocity of waterjet, mass flow rate, and stand-off distance of the nozzle against the response such as cutting time and sub-surface delamination of layers were studied. The delamination was measured using the variation in thickness before and after the cutting process. The changes in the cutting surface were analyzed using macroscopic analysis. The study also developed the regression model and conducted ANOVA on generated data. Grey Relational Analysis (GRA) was used to identify the optimum values of input process parameters against multiple responses such as cutting time and delamination. The results revealed that the jet velocity significantly affected the cutting time, whereas the stand-off distance and mass flow rate affected the delamination thickness of the laminates. A slight plastic deformation was noted on the metal surfaces along with irregularities and fiber exposure was observed in the GFRP layers of laminates exhibited low cutting performance.