High strength, excellent corrosion resistance, and low density are the main properties that make titanium attractive for a variety of applications such as the production of airframes, engine components, steam turbine blades, superconductors, missiles, etc. Machining of titanium alloy by conventional machines causes the problems such as chipping and premature tool failure, deflections of the work-piece, increases the temperature at the tool-work piece interface, etc. Hence under such circumstances, nonconventional Die sink Electrical Discharge Machining (EDM) process can be alternative to overcome such problems. The primary aim of this paper is to investigate the effects of process parameters (factors) on material removal rate (MRR) in the EDM process. The process parameters considered for this investigation are current (C), voltage (V), pulse on time (Ton), and pulse off time (Toff) for EDM machining of titanium (grade-2) alloy with copper as an electrode material. The experiments were designed with the Taguchi method, orthogonal array L9. The maximum MRR obtained was 0.073 mm3/min with the voltage of 40 V, current of 8A, pulse on at 60 µs, and pulse off at 9 µs respectively. While the secondary aim of this research is to investigate the effect of process parameters on fatigue strength of titanium (grade-2) alloy. During fatigue test it was observed, fatigue strength decreases with an increase in current and pulse on time.