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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 (<i>Ra</i>) concerning the thickness of the workpiece. Three different thicknesses were cut under different conditions; the <i>Ra</i> 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 <i>Ra</i>. The ANN’s model was validated using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula>-fold cross-validation. A lowest test root mean squared error (RMSE) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.2084</mn></mrow></semantics></math></inline-formula> was achieved. The results of the predicted <i>Ra</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>95</mn></mrow></semantics></math></inline-formula>% 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 <i>Ra</i>. Its main advantage is the reduced time needed for experimentation.