Due to its high corrosion resistance and low density, it is tedious to machine high strength materials such as titanium alloy for the manufacture of engineering products related to aerospace, automobiles, and medical applications. In this study, an attempt was made to consider the impact of tool electrodes in the electrical discharge machining method for successful machinability of titanium alloy. High temperatures are used during electrical discharge machining to melt and vaporise the hard titanium alloy. In the current work, an EDM machining method was used to machine a Ti-6Al-2Sn-4Zr-2Mo alloy while using the input parameters of pulse on time, voltage, and current as process parameters. The experiments were carried out based on the workpiece, and surface morphology was performed on the workpiece surface. The process parameters were optimised using the Multi-Response Grey Relation Analysis method, and a major effects plot was created to see how the factors affected the MRR and surface roughness. Surface finish and MRR have been discovered to be directly correlated with discharge current. These are the best process parameters for machining pulse on time (150 s), voltage (60 V), and discharge current (16 A).