This study investigates how key drilling parameters—feed rate (f), spindle speed (N), and drill diameter (d)—affect the delamination factor (Fd) during the machining of the Flower stalk of Agave americana (FSAa) fiber-reinforced biocomposites, using High-Speed Steel (HSS) and High-Speed Steel Coated with Titanium (HSS-TiN) tools. The experimental results show that increasing f and d leads to a decrease in Fd, reaching a minimum of 1.074 with the HSS tool compared to 1.020 with the HSS-TiN (N = 800 rpm, f = 150 mm/min, d = 5 mm). Conversely, a higher rotational speed slightly reduces delamination, with a maximum Fd of 1.204 obtained with HSS-TiN (N = 1600 rpm, f = 50 mm/min, d = 10 mm), compared to 1.261 for HSS under the same conditions. A comparative analysis shows that the HSS-TiN tool consistently outperforms the uncoated HSS tool, offering lower delamination levels due to reduced friction and better wear resistance. Modeling with response surface methodology (RSM) and artificial neural networks (ANN) was developed to predict Fd, with both models showing excellent agreement with experimental data. For HSS-TiN, the ANN model achieved a coefficient of determination R² of 98.94%, surpassing that of the RSM model, which was 98.11%. Similarly, for HSS, ANN obtained an R2 of 98.82%, slightly higher than that of RSM (98.04%), thus confirming the superior predictive capacity of the neural approach in both cases. The optimized numerical model for the delamination factor of the biocomposite using HSS-TiN tool showed the lowest delamination factor of 1.019 for a drill diameter of 9.97 mm, a feed rate of 138.59 mm/min and a spindle speed of 817.04 rev/min. The findings highlight the potential of surface-coated tools and advanced modeling techniques in improving drilling quality for sustainable composite materials.