Servicing aircraft engines sometimes requires manufacturing only a single piece of a given part. Manufacturing a turbine disc using traditional methods is uneconomical. It is necessary to use a different machining method recommended for small lot production. One of the proposed methods is WEDM (wire electrical discharge machining). The article presents the results of the research on finishing WEDM of Inconel 718 turbine disc fir tree slots. The influence of infeed, mean gap voltage, peak current, pulse off-time, and discharge energy on the shape accuracy, surface roughness, microcracks, and the white layer thickness were determined. Mathematical models were developed based on the DoE (Design of Experiment) analysis. The statistical significance of the models was verified with the ANOVA (Analysis of Variance) test. The machining parameters control methods that allow achieving the required shape accuracy, surface roughness, and surface layer condition were presented. The obtained surface roughness was Ra = 0.84 μm, the shape accuracy of the slot in the normal-to-feed direction was Δd = 0.009 μm, the profile shape accuracy was Δr = 0.033 μm, and the thickness of recast (white) layer was approximately 5 μm.