Estimation of machining time and accuracy plays a pivotal role in exemplifying the efficacy of the wire electric discharge machining (WEDM) process. The comprehensive insight on the influence of servo feed rate under different control modes (proportional control mode, constant feed mode, and constant voltage mode) on the machining time (MT), corner error (CE), and radius of the concave profile (RUC) of a convex–concave-based geometrical profile was discussed in the present research venture. Moreover, the influence of other process variables such as dielectric water pressure (WP), wire tension (WT), and servo voltage (SV) on the responses was also included in the present research. A face-centered central composite design strategy was employed to plan the experiments. The ANOVA test analyzed that SV and SF are the influential parameters for all the responses. Unlike the MT and RUC, the dielectric water pressure (WP) and wire tension (WT) were also found to influence the CE from the ANOVA analysis. Contour plots were exhibited to reveal the interaction effect between servo feed rate and servo voltage on the responses. Finally, the desirability function with the Nelder–Mead simplex algorithm was exploited to optimize the three responses simultaneously. The optimal settings determined by the proposed approach were as follows: WP = 15 kg/cm2, WT = 12 N, SV = 60 V, and SF = 2150 mm/min. FESEM micrographs and images from non-contact optical profilometry were showcased for different servo settings to demonstrate the role of servo parameters on the machined surfaces.