Electrical Discharge Machining (EDM) consists of a non-conventional machining process, which is widely used in modern industry, and especially in machining hard-to-cut materials. By employing EDM, complex shapes and geometries can be produced, with high dimensional accuracy. Titanium alloys, due to their unique inherent properties, are extensively utilized in high end applications. Nevertheless, they suffer from poor machinability, and thus, EDM is commonly employed for their machining. The current study presents an experimental investigation regarding the process of Ti–6Al–4V ELI with high power EDM, using a graphite electrode. Control parameters were the pulse-on current (Ip) and time (Ton), while Machining performances were estimated in terms of Material Removal Rate (MRR), Tool Material Removal Rate (TMRR), and Tool Wear Ratio (TWR). The machined Surface Roughness was calculated according to the Ra and the Rt values, by following the ISO 25178-2 standards. Furthermore, the EDMed surfaces were observed under optical and SEM microscopy, while their cross sections were also studied in order the Average White Layer Thickness (AWLT) and the Heat Affected Zone (HAZ) to be measured. Finally, for the aforementioned indexes, Analysis Of Variance was performed, whilst for the MRR and TMRR, based on the Response Surface Method (RSM), semi-empirical correlations were presented. The scope of the current paper is, through a series of experiments and by employing statistical tools, to present how two main machining parameters, i.e., pulse-on current and time, affect major machining performance indexes and the surface roughness.