This work presents a comprehensive research using the Taguchi method and response surface methodology (RSM) to predict surface roughness parameters in wire electrical discharge machining (WEDM) manufacturing for a novel Ti–Al intermetallic based composite that was developed at Supmeca, a composite design laboratory for aeronautical applications in Paris, France. At the first stage, a detailed microstructure analysis was carried out on this composite. After that, the cutting parameters of the WEDM process were determined: Start-up voltage U, Pulse-on-time Ton, speed advance S and flushing pressure p were selected to find out their effects on surface roughness Ra. In the second stage, analyses of variance (ANOVA) were used as the statistical method to define the significance of the machining parameters. After that, an integrated method combining the Taguchi method and the response surface methodology (RSM) was used to develop a predictive model of the finish surface. The microstructure of the surface and subsurface of the cut edge, the micro-cracks, debris and craters and surface roughness of the specimens cut at the altered conditions were evaluated by scanning electron microscopy (SEM) and 3D-Surfscan.