Vent holes in tire molds typically exhibit large depth-to-diameter ratios (25–50) and variable drilling angles, both of which increase the risk of drill-bit breakage during automated drilling. To address this problem, this study develops a robotic drilling system consisting of a 6-DOF industrial robot and a dedicated end effector integrating a spindle unit, a linear feed unit, and a telescopic drill-bushing unit. A GRU-based feed-torque model predictive control method (GFTMPC) is proposed for robotic small-diameter deep-hole drilling, which achieves flexible control by integrating angle-aware feed-torque modeling with constrained MPC-based feed-rate optimization. The resulting GRU-based feed-torque model (GFTM) is embedded in the MPC framework for torque prediction and achieves an R² value of 0.9682. Under identical simulation conditions, GFTMPC reduces the RMSE of the feed-rate increment by 34.82% and the saturation ratio of the feed-rate increment by 90.78% relative to a PID baseline, indicating smoother feed regulation and fewer abrupt control actions in simulation. Comparative engineering experiments further suggest that, under the tested robotic configurations, adaptive feed-rate regulation by GFTMPC is an important contributor to improved tool life and drilling reliability. Hole-diameter measurements show deviations ranging from +0.03 mm to +0.11 mm, which were considered acceptable for the subsequent work steps in this application. Engineering application results show that robotic drilling increases daily throughput per worker by 71.38% and the average number of holes drilled per bit by 237%.