Plastics reinforced with glass fiber have a significant likelihood of being replaced by natural fiber hybrid composites (NFHCs). Making holes helps in part assembly, which is a crucial activity in the machining of composite constructions. As a result, choosing the right drill bit and cutting parameters is crucial to creating a precise and high-quality hole in composite materials. The present study employs the Taguchi approach to examine the delamination behavior and hole quality of ramie–bamboo composite laminates consisting of epoxy and nano-fillers (SiC, Al₂O₃) with feed, spindle speed, and three distinct drill bit types. Surface roughness and delamination are significantly influenced by feed and spindle speed, as indicated by the results of the analysis of variance. It was found that the spindle speed had a major impact on the delamination factor and surface roughness, while the feed and drill bit type had a minor influence. The surface roughness (76.5%) and delamination factor (66.7%) are significantly affected by the spindle speed.