Machining of accurate geometrical profiles like triangles, squares or circles with good surface finish and high productivity in metal matrix composites is required for various industrial applications. Thermoelectic principle-based wire electric discharge machine (WEDM) can be conventionally used to overcome the difficulty which occurs during the machining of composites due to the presence of hard abrasive particles. Therefore, in this investigation, three geometrical profiles possessing equal perimeters were produced in 5 mm thick aluminum metal matrix composites (AMMCs) by WEDM. In order to analyze the effect of reinforcements three different AMMCs containing Al6061 as a matrix were produced by stir casting method. The fabricated composites, respectively, contain 10% alumina ([Formula: see text]), 10% silicon carbide (SiC) and a mixture of 5% [Formula: see text] with 5% SiC. The individual effect of various input parameters like pulse-on time ([Formula: see text] = 30-50 [Formula: see text]s), pulse-off time ([Formula: see text] = 6–12 [Formula: see text]s), current ([Formula: see text] = 1–5 A) and geometrical shapes (circle, triangle, and square) on cutting velocity (CV) and surface roughness (SR) were investigated. Furthermore, parametric analysis using regression models was also performed to evaluate the simultaneous effect of two interacting parameters on CV and SR. The study reveals that in the case of hybrid composite, CV decreases with [Formula: see text] and SR is always higher for triangular profiles when [Formula: see text] and [Formula: see text] change. The regression plots indicate that the interaction effect of [Formula: see text] × [Formula: see text] plays a major role in CV for all three composites. Multiobjective optimization using a composite desirability approach reveals a marginal increase in CV (8.58%) and a significant reduction (57.72%) in SR at optimal input parameters for Al6061–10% SiC. The morphological analysis at optimal input parameters indicates a significant reduction in resolidified metal drops and microcraters.