Incoloy 925, a Nikel-based superalloy, exhibits low machinability with conventional machining techniques due to its inhomogeneous properties. Therefore, there is a need to establish a non-conventional method to efficiently machine this alloy. This work is a novel attempt to present the electric discharge machining (EDM) of the superalloy Incoloy 925 and subsequent multi-response optimization. The model for the analysis was designed using the Box Behnken Design (BBD) technique, and the Response Surface Methodology (RSM) was used for the optimization of the results. The machining was performed using a cylindrical copper tool of 11 mm diameter. The effect of pulse-on time (Ton), current, and pulse-off time (Toff) on the material removal rate (MRR), tool wear rate (TWR), and surface roughness (SR) was investigated. The results from variance analysis confirmed the significance of all the three input factors. The investigation revealed that the maximum MRR (99.2154 mm3/min) was obtained at a pulse-on time of 90 µs, pulse-off time of 5 µs, and current of 30 A. The minimum TWR (0.8866 mm3/min) were achieved at Ton = 60 µs, Toff = 8 µs and current = 10 A. The microscopic images of the machined surfaces revealed very few micro-voids and globules and no cracks, resulting in a fine surface finish of 1.2436 µm, achieved through optimal discharge energy transfer and copper electrodes. The optimal values MRR, TWR, and SR according to composite desirability function are 99.1524 mm3/min, 1.0915 mm3/min, and 1.3925 µm. The experimental results were accurately predicted using RSM and an artificial neural network (ANN), with the ANN showing a predicted correlation coefficient (R) close to 1 indicating high accuracy of the model.