Electrical Discharge Machining (EDM) is one of the most basic non-conventional machining processes for production of complex geometries and process of hard materials, which are difficult to machine by conventional process. It is capable of machining geometrically complex or hard material components, that are precise and difficult-to-machine such as heat-treated tool steels, composites, super alloys, ceramics, carbides, heat resistant steels etc. The present study is focusing on the die sinking electric discharge machining (EDM) of AISI H 13, W.-Nr. 1.2344 Grade: Ovar Supreme for finding out the effect of machining parameters such as discharge current (GI), pulse on time (POT), pulse off time (POF) and spark gap (SG) on performance response like Material removal rate (MRR), Surface Roughness (Ra) & Overcut (OC) using Square-shaped Cu tool with Lateral flushing. A well-designed experimental scheme is used to reduce the total number of experiments. Parts of the experiment are conducted with the L9 orthogonal array based on the Taguchi methodology and significant process parameters are identified using Analysis of Variance (ANOVA). It is found that MRR is affected by gap current & Ra is affected by pulse on time. Moreover, the signal-to-noise ratios associated with the observed values in the experiments are determined by which factor is most affected by the responses of MRR, Ra and OC. These experimental data are further investigated using Grey Relational Analysis to optimize multiple performances in which different levels combination of the factors are ranked based on grey relational grade. The analysis reveals that substantial improvement in machining performance takes place following this technique.