Electrical discharge machining (EDM) is much preferred in modern precision-manufacturing industries owing to its ability to machine any metal regardless of its hardness. However, its constraint is that the selected metal should be an electrically conductive material. For the present investigation, an Inconel 718 alloy was selected for EDM, using a TiB2-Cu electrode made with powder metallurgy. Input factors, namely, the pulse current (Ip), pulse-on time (Ton) and gap voltage (Gv) were selected and their output responses were the surface roughness (SR) and material-removal rate (MRR). For the response surface, the Box Behnken technique was preferred when designing the experiments (DoE). An ANOVA test was performed to understand the influence of the selected input factors on the SR and MRR. The RSM integrated with a grey relational analysis (GRA) revealed that the optimal input parameters for better machining characteristics were: Ip = 10 A, Ton = 40 µs and Gv = 50 V. Besides, the results also showed that the pulse current more significantly influenced the output responses than the other parameters. Moreover, an increase in the gap voltage caused surface irregularities on the machined surface. Surface morphology of the machined surfaces was analysed through SEM and EDAX. Moreover, a certain amount of tool-material transfer was noted with the EDAX analysis.