A nickel-based copper alloy known as Monel-400 is extensively applied in many industries including aerospace, marine engineering, and nuclear power generation, owing to its exceptional characteristics such as extreme tensile strength and toughness, excellent corrosion resistance, and the ability to retain shape even at extremely high temperatures. Traditional methods of drilling Monel-400 alloy are difficult due to quick tool wear and poor surface polishing, resulting in expensive machining costs. In this study, a technique called heat annealing was implemented to externally heat-treat the Monel-400 alloy material before the drilling process. Cutting force, surface roughness, and tool wear were used as the responses to investigate the effect of heat annealing and the drilling parameters on the machinability of Monel-400. The results revealed that the cutting force (Fz) and surface roughness (Ra and Rt) could be reduced by 33%, 31%, and 25%, respectively, after annealing at 700 °C compared to the results of the drilled Monel-400 at room temperature. It can be observed that the maximum improvement can reach 42% of Fz, 35% of Ra, and 59% of Rt while annealing Monel-400 at 1000 °C. A significant reduction was observed in the tool wear for machining the annealed material, which minimized the tooling and overall machining cost. Regarding the effects of the drilling process on the considered responses, the results revealed that the spindle speed has a greater effect on the cutting force, whereas the feed rate has the most significant effect on Ra. The significance of the drilling input parameters on the outputs is determined by analysis of the main effect plots and surface plots. Subsequently, the multi-objective genetic algorithm (MOGA) is used to identify the optimal parametric conditions for minimizing the cutting force and surface roughness of the drilled holes. The optimized values achieved via multi-objective optimization are the cutting force, Fz = 388–466 N, and the surface roughness, Ra = 0.17–0.19 μm and Rt = 3–3.5 μm, respectively.