The use of multiwall carbon nanotube (MWCNT) reinforced polymer nanocomposites have significant importance since MWCNT enhances the aspect ratio and interface conditions of polymer materials. However, the machining aspects of carbon nanofillers are still a potential area of research. The mechanical and electrical properties of MWCNT/epoxy nanocomposites makes it a suitable alternative to conventional engineering materials. This work focused the machining characteristics optimization during drilling of MWCNT/epoxy nanocomposites using TOPSIS and GRA theory. The machining characteristics are considered which are surface roughness, torques and thrust. By using both the multi-criteria optimization techniques, all the machining characteristics aggregated into the single objective function. The effects of drilling parameters have been investigated by variance analysis. The outcomes of both the proposed module give different optimal conditions of process parameters. The confirmatory experiment carried out to validate the obtained results, and it has been observed that GRA is more feasible than TOPSIS. During machining, the cutting force rises with the high feed rate, and the lower value of feed rate reduces the surface roughness. The achieved improvements in drilling performances are highly required for an efficient machining environment. Further, a microstructural investigation was done to check the quality of the machined samples.