The unconventional technology of wire electrical discharge machining is widely used in all areas of industry. For this reason, there is always an effort for efficient machining at the lowest possible cost. For this purpose, the following comprehensive study has been carried out to optimize the machining of the copper alloy Ampcoloy 35, which is particularly useful in plastic injection moulds. Within the study, a half-factor experiment of 25-1 with 10 axial points and seven central points of a total of 33 rounds was carried out, which was focused on the response monitoring of the input factors in the form of the machine parameters setup: gap voltage, pulse on time, pulse off time, discharge current, and wire speed. Based on the study of the response in the form of cutting speed and surface topography, their statistical models were created, while the optimal setting of machine parameters was determined to maximize the cutting speed and minimize the topography parameters. Further, a detailed cross-sectional analysis of surface and subsurface layer morphology was performed using electron microscopy including chemical composition analysis. In order to study microstructural changes in the material at the atomic level, a lamella was created, which was then studied using a transmission electron microscope.