Wire—electrical discharge machining (W-EDM) is a precise and efficient non-traditional technology employed to cut intricate shapes in conductive biomaterials. These biomaterials are challenging to machine using traditional methods. This present study delves into the impact of various process parameters, namely discharge duration (Ddur), spark gap time (Stime), discharge voltage (Dvolt), and wire advance rate rate (Wadv). This research evaluates the impact of several factors on response variables, namely the machining rate (MR) and surface irregularity (SR), during the machining process of the AM60B magnesium alloy. The confirmation of the material used in the machining process is achieved via the utilisation of a scanning electron microscopy (SEM) image in conjunction with an energy dispersive spectroscopic (EDS) image. The experiment is designed as L9 orthogonal array by using Taguchi's approach, taking into account 4 factors with 3 levels. The objective of this experiment is to ascertain the most favourable values for machining parameters while working with AM60B magnesium alloy using brass wire. Through analysis of variance (ANOVA), the study confirms that wire advance rate (43.10%) is the most influencing parameter for machining rate and surface irregularity followed by spark gap time (33.91%) and discharge duration (11.48%). Additionally, The TOPSIS-CRITIC and the desirability approach were used in order to determine the optimum parameter combinations that provide the most favourable combined output. Confirmatory testing is used to evaluate the efficiency of the stated ideal conditions. The maximum improvement in Desirability approach is obtained at 4.56% and 4.193% for MR and SR respectively. The maximum improvement in TOPSIS approach is obtained at 1.77% and 2.78% for MR and SR respectively.