Wire electrical discharge machining (WEDM) is an unconventional machining technology that can be used to machine materials with minimum electrical conductivity. The technology is often employed in the automotive industry, as it makes it possible to produce mold parts of complex shapes. Copper alloys are commonly used as electrodes for their high thermal conductivity. The subject of this study was creating mathematical models for the machining optimization of Ampcoloy 35 with different thicknesses (ranging from 5 to 160 mm with a step of 5 mm) using WEDM to improve the surface properties of the mold parts. The Box–Behnken type experiment was used with a total of 448 samples produced. The following machining parameters were altered over the course of the experiment: the pulse on and off time, discharge current, and material thickness. The cutting speed was measured, and the topography of the machined surfaces in the center and at the margins of the samples was analyzed. The morphology and subsurface layer were also studied. What makes this study unique is the large number of the tested thicknesses, ranging from 5 to 160 mm with a step of 5 mm. The contribution of this study to the automotive industry and plastic injection mold production is, therefore, significant. The regression models for the cutting speed and surface topography allow for efficient defect-free machining of Ampcoloy 35 of 5–160 mm thicknesses, both on the surface and in the subsurface layer.