Hole quality in composite materials is gaining interest in aerospace, automotive, and marine industries, especially for structural applications. This paper aims to investigate the quality of holes performed without a backup plate, in thin plates of glass fiber-reinforced polymer (GFRP). The samples were manufactured by two different technologies: vacuum bagging and an innovative method named vacuum mold pressing. Three experiments were designed choosing the control factors that affect the maximum cutting force, delamination factor, and surface roughness of drilled holes in composite materials based on twill fabric layers. Quality analysis of the hole features was performed by microscopy investigations. The effects of the main factors on the targets are investigated using the statistical design of experiments, considering control factors, such as support opening width, weight fraction (wf), feed per tooth, and hole area. The results showed that the feed per tooth and hole area had a more significant influence on the delamination factors and surface roughness (Sa). The best quality of the holes drilled in twill-based GFRP was achieved for a lower feed rate of 0.04 mm/tooth and used a support opening width of 55 mm.