The study’s primary purpose was to explore the abrasive water jet (AWJ) cut machinability of stainless steel X5CrNi18-10 (1.4301). The study analyzed the effects of such process parameters as the traverse speed (TS), the depth of cut (DC), and the abrasive mass flow rate (AR) on the surface roughness (Ra) concerning the thickness of the workpiece. Three different thicknesses were cut under different conditions; the Ra was measured at the top, in the middle, and the bottom of the cut. Experimental results were used in the developed feed-forward artificial neural network (ANN) to predict the Ra. The ANN’s model was validated using k-fold cross-validation. A lowest test root mean squared error (RMSE) of 0.2084 was achieved. The results of the predicted Ra by the ANN model and the results of the experimental data were compared. Additionally, as TS and DC were recognized, analysis of variance at a 95% confidence level was used to determine the most significant factors. Consequently, the ANN input parameters were modified, resulting in improved prediction; results show that the proposed model could be a useful tool for optimizing AWJ cut process parameters for predicting Ra. Its main advantage is the reduced time needed for experimentation.