In the present study, a comprehensive parametric analysis was carried out using the electrical discharge machining of Ti6Al4V, using pulse-on time, current, and pulse-off time as input factors with output measures of surface roughness and material removal rate. The present study also used two different nanopowders, namely alumina and nano-graphene, to analyze their effect on output measures and surface defects. All the experimental runs were performed using Taguchi’s array at three levels. Analysis of variance was employed to study the statistical significance. Empirical relations were generated through Minitab. The regression model term was observed to be significant for both the output responses, which suggested that the generated regressions were adequate. Among the input factors, pulse-off time and current were found to have a vital role in the change in material removal rate, while pulse-on time was observed as a vital input parameter. For surface quality, pulse-on time and pulse-off time were recognized to be influential parameters, while current was observed to be an insignificant factor. Teaching–learning-based optimization was used for the optimization of output responses. The influence of alumina and nano-graphene powder was investigated at optimal process parameters. The machining performance was significantly improved by using both powder-mixed electrical discharge machining as compared to the conventional method. Due to the higher conductivity of nano-graphene powder, it showed a larger improvement as compared to alumina powder. Lastly, scanning electron microscopy was operated to investigate the impact of alumina and graphene powder on surface morphology. The machined surface obtained for the conventional process depicted more surface defects than the powder-mixed process, which is key in aeronautical applications.