Shape memory alloy (SMA), particularly those having a nickel–titanium combination, can memorize and regain original shape after heating. The superior properties of these alloys, such as better corrosion resistance, inherent shape memory effect, better wear resistance, and adequate superelasticity, as well as biocompatibility, make them a preferable alloy to be used in automotive, aerospace, actuators, robotics, medical, and many other engineering fields. Precise machining of such materials requires inputs of intellectual machining approaches, such as wire electrical discharge machining (WEDM). Machining capabilities of the process can further be enhanced by the addition of Al2O3 nanopowder in the dielectric fluid. Selected input machining process parameters include the following: pulse-on time (Ton), pulse-off time (Toff), and Al2O3 nanopowder concentration. Surface roughness (SR), material removal rate (MRR), and recast layer thickness (RLT) were identified as the response variables. In this study, Taguchi’s three levels L9 approach was used to conduct experimental trials. The analysis of variance (ANOVA) technique was implemented to reaffirm the significance and adequacy of the regression model. Al2O3 nanopowder was found to have the highest contributing effect of 76.13% contribution, Ton was found to be the highest contributing factor for SR and RLT having 91.88% and 88.3% contribution, respectively. Single-objective optimization analysis generated the lowest MRR value of 0.3228 g/min (at Ton of 90 µs, Toff of 5 µs, and powder concentration of 2 g/L), the lowest SR value of 3.13 µm, and the lowest RLT value of 10.24 (both responses at Ton of 30 µs, Toff of 25 µs, and powder concentration of 2 g/L). A specific multi-objective Teaching–Learning-Based Optimization (TLBO) algorithm was implemented to generate optimal points which highlight the non-dominant feasible solutions. The least error between predicted and actual values suggests the effectiveness of both the regression model and the TLBO algorithms. Confirmatory trials have shown an extremely close relation which shows the suitability of both the regression model and the TLBO algorithm for the machining of the nanopowder-mixed WEDM process for Nitinol SMA. A considerable reduction in surface defects owing to the addition of Al2O3 powder was observed in surface morphology analysis.