Wire electrical discharge machining (WEDM) is widely preferred for machining difficult-to-cut materials like Ti6Al4V. In the present study, current, pulse-off-duration (Toff), and pulse-on-duration (Toff) were identified as vital input factors for the WEDM process of Ti6Al4V. Material removal rate (MRR) and surface roughness (SR) were selected as output measures for the study. The experiments were carried out by employing Taguchi’s L9 design at three levels. Empirical models were generated, which give the relationship between the input and output factors of the process. To check the acceptability of the model terms, analysis of variance (ANOVA) was used. The regression mode was observed to be significant for the output measures. For MRR, Toff was recorded as the highly significant factor affecting the response values with 74.95% impact, followed by Ton with 16.39%, and current with 6.56%. In the case of SR, Ton was found to be a highly significant factor with a 50.24% impact, followed by current with 43.99%, and Toff with 1.47%. Further, multi-objective optimization by using the HTS technique was performed. The effect of expanded graphite (EG) nano-powder has been studied on the output factors of MRR and SR. The use of EG nano-powder was found to improve WEDM operations as MRR was increased by 45.35%, and simultaneously, SR was reduced by 36.16%. Lastly, the surface morphology of the machined surface was investigated by employing SEM to understand the effect of EG nano-powder. The results have shown a reduction in surface defects by using EG nano-powder compared to the conventional WEDM process.