Ti-6Al-4V is considered a challenging material in terms of accurate machining. Therefore, electric discharge machining (EDM) is commonly engaged, but its low cutting rate depreciates its use. This issue is resolved if graphene nanoparticles are mixed in the dielectric. However, the control over the sparking phenomenon reduces because of the dispersion of graphene particles. Subsequently, the machined profile’s geometric accuracy is compromised. Furthermore, the presence of nanographene induces different sparks along axial and radial cutting orientations. This aspect has not been comprehensively examined yet and dedicatedly targeted in this study to improve the quality of EDM process for Ti-6Al-4V. A total of 18 experiments were conducted under Taguchi’s L18 design considering six parameters namely, electrode type, polarity, flushing time, spark voltage, pulse time ratio, and discharge current. The aluminum electrode proved to be the best choice to reduce the errors in both the cutting orientations. Despite the other parametric settings, negative tool polarity yields lower values of axial (ADE) and radial errors (RDE). The developed optimal settings ensure 4.4- and 6.3-times reduction in RDE and ADE, respectively. In comparison to kerosene, graphene-based dielectric yields 10.2% and 19.4% reduction in RDE and ADE, respectively.