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Due to its inherent properties, Ti64 has set many challenges in industries during its machining using conventional machining processes. Traditional machining of Ti64 is not a feasible option considering the economic and environmental perspectives. Non-conventional techniques like electrical discharge machining (EDM) are promising methods for machining Ti64 despite challenges like higher tool wear and lower machining rates. The current paper investigated the erosion rates while machining Ti64 using deep cryo-treated electrodes. The peak current (I_p), pulse on time (T_on) and gap voltage (V_g) were used as control parameters while investigating erosion rates, viz., Material Removal Rate (MRR) and Tool Wear Rate (TWR). Experiments were planned according to the RSM-based Central Composite Design (CCD). Considering the multi-objective nature of the current problem, Grey Relational Analysis (GRA) has been incorporated to find a single parametric condition that will satisfy both MRR and TWR. Peak current, ${\mathrm{\text{I}}}_{\mathrm{\text{p}}}=24$A, Pulse On time, ${\mathrm{\text{T}}}_{\mathrm{\text{on}}}=150$$\mu$s and Gap voltage, ${\mathrm{\text{V}}}_{\mathrm{\text{g}}}=70$V was found to be the optimal setting giving $\mathrm{\text{MRR}}=1.367$mm³/min and $\mathrm{\text{TWR}}=0.170$mm³/min. Furthermore, topographical analysis of the EDMed surfaces has been performed using SEM, XRD and 3D optical profilometry techniques to characterise the surface and to investigate the possibility of other intermetallic compounds formed on the machined surface.