This paper aims to optimize the quality characteristics of the drilling process in glass fiber-reinforced polymer (GFRP) composites. It focuses on optimizing the drilling parameters with drill point angles concerning delamination damage and energy consumption, simultaneously. The effects of drilling process parameters on machinability were analyzed by evaluating the machinability characteristics. The cutting power was modeled through drilling parameters (speed and feed), drill point angle, and laminate thickness. The response surface analysis and artificial neural networks enhanced by the particle swarm optimization algorithm were applied for modeling and evaluating the effect of process parameters on the machinability of the drilling process. The most influential parameters on machinability properties and delamination were determined by analysis of variance (ANOVA). A multi-response optimization was performed to optimize drilling process parameters for sustainable drilling quality characteristics. The obtained models were applied to predict drilling process characteristics, and exhibited an excellent harmony with the experiment results. The optimal drilling process factors were the highest spindle speed and the lowest feed, with a drill point angle of 118° for the laminate of 4.75 mm thickness.