Abstract: The nonlinear error of cutting slits in abrasive water jet (AWJ) cutting of thick plates affects machining accuracy. To improve processing precision, this study investigates the influence and interaction mechanisms of four key process parameters—abrasive flow rate, jet pressure, cutting quality grade, and material thickness—on the convexity-index of Al6061-T6 thick aluminum alloy plates. Using convexity-index as the response variable, data were processed with Minitab software and analyzed through multiple methods to establish a regression model. Results indicate that material thickness is the dominant factor affecting convexity-index, contributing 50.8% of the variance. The parameter influence weights are ranked as: material thickness > cutting quality grade > jet pressure > abrasive flow rate. The impact patterns show that convexity-index decreases with increasing material thickness and cutting quality grade, while increases with rising jet pressure. The minimum convexity-index is achieved when abrasive flow rate is 4, jet pressure is 315 MPa, cutting quality grade is 10, and material thickness is 150 mm.