The present paper identifies the different process parameters that effect the cutting speed and surface roughness in wire electrical discharge machining of Titanium-6-2-4-2 (HSTR aerospace alloy), which is so far not reported in the literature. It also identifies optimal process parameter combination for simultaneous optimization of cutting speed and surface roughness to be presented as a guideline for machining of Titanium-6-2-4-2. Box–Behnken design and response surface methodology are used to plan and analyse the experiments. Six control factors viz. Pulse on time, pulse off time, peak current, spark gap set voltage, wire feed, and wire tension are chosen as process parameters to study the performance of the process in terms of cutting speed and surface roughness. The recommended optimal parameter combinations have been verified by conducting confirmation experiments.