Shape Memory Alloys (SMAs) are known for their unique properties such shape memory effect and superelasticity along with biocompatibility, good ductility, corrosion and wear resistance and better fatigue strength. NiTi alloys are the most important Shape Memory alloys, which are immensely used in various fields of science. The machining of these difficult to cut alloys by conventional machining processes poses various difficulties and brings about changes in the properties of material. Hence, varieties of non-conventional machining techniques have been employed. Wire Electric Discharge machining is one of these non-conventional machining processes, which is used for machining of all conductive materials and intricate shapes. In the present study, the Wire EDM characteristics of Ti50Ni48Co2 have been studied. The effect of various process parameters such as Pulse on time, Pulse off Time and Servo Voltage on the machining characteristics such as Material removal rate (MRR) and Surface Roughness (SR) have been investigated. The experiments were designed as per Taguchi L9 Orthogonal Array. The input parameters are also optimized using Multi-objective Grey Relational Analysis (GRA) in order to maximize MRR and minimize SR simultaneously. Pulse on Time (Ton) =125µs, Pulse off Time (Toff) =35µs and Servo Voltage (SV) =40V were found as a best combination of process parameters for machining of Ti50Ni48Co2 alloy to achieve the higher MRR with better surface roughness. The characterization of the machined surface has been carried out with respect to microstructure, recast layer thickness and microhardness at the optimized process parameters. Micro cracks, micro globules were noticed on the machined surface and harder surface has been found near the machined surface during the microhardness analysis.