Electrochemical machining (ECM) process has unique capabilities to offer a better alternative and sometimes is considered the only available option to cut or create intricate profiles into hard materials. ECM is a mirror-shaped-process; i.e., the shape developed into the workpiece is a mirror image to the tool profile. This study presents an application of using copper wire as a tool to create peripheral grooves. This method saves time and cost of profiling the cathode as a mirror image of the predetermined workpiece shape. This article discusses the influences of input parameters—wire feed rate, wire diameter, and workpiece rotational speed—on the responses, frontal gap, metal removal rate, specific power consumption, and groove geometry, using response surface methodology (RSM). Mathematical models were developed for the aforementioned responses, and their adequacies were checked using analysis of variance (ANOVA). The process could be optimized to create predetermined groove with a specific width; for example, the optimum values of feed rate, wire diameter, and workpiece speed are 0.07 mm/min, 2.3 mm, and 450 rpm, respectively, to maximize the MRR and minimize the specific power consumption in order to create a groove of 9.4 mm in width.