The machining of Nitinol shape memory alloys (SMA) through conventional machining techniques imposes several challenges due to the alloys’ comprehensive mechanical qualities. Wire electrical discharge machining (WEDM) process is a non-conventional machining technique that is suitable mainly for producing complex shape geometries with excellent surface features for difficult-to-cut materials. The current study attempted the use of a near-dry WEDM process for Nitinol SMA with the consideration of multiple response variables. The studied literature and machine capabilities have identified input factors of pulse-on-time (Ton), pulse-off-time (Toff), and current and output factors of MRR, SR, and RLT. Through the Taguchi approach, a total of nine experimental trials were designed to analyze the performance of the process. The statistical significance of input factors on the performance measures was studied with the help of ANOVA techniques. Statistical analysis for all the output measures has shown that the generated regression terms had a significant influence. For single output measures, the current was found to have a substantial effect on both MRR and SR, while Toff was the most significant contributor in the case of RLT. The obtained results of residual plots for all performance measures implied good ANOVA results. The effect of near-dry WEDM variables was studied on output measures through main effect plots. Grey relational analysis (GRA) has been employed to attain optimal parametric settings of multiple performance measures. GRA technique for the optimal parametric settings of simultaneous performance measures of MRR, SR, and RLT was found to have a Ton of 30 µs, Toff of 24 µs, and current of 4 A. Validation trials were conducted to check the adequacy of the GRA technique. The minor acceptable deviation was recorded among the anticipated and recorded values. This clearly reveals the acceptability of the integrated approach of the Taguchi–Grey method. The surface morphology for the near-dry and wet-WEDM has also been investigated through scanning electron microscopy (SEM). The author considers that the present study will be beneficial for users working in WEDM and near-dry WEDM processes for hard machining materials.