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Refractory high entropy alloys (RHEAs) with multiple principal elements constitute a new paradigm in alloy design and have gained recent interest for advanced technical applications due to their unique properties and mechanical stability at high temperatures. However, the refractory metals that make up these alloys are pretty expensive, and they cause RHEAs to exhibit low plasticity behaviour at room temperature. The high stability properties of RHEAs from room temperature to high temperatures limit their machinability with traditional cutting methods. Therefore, it is vitally important to economically machine these alloys while preserving their mechanical properties and minimising waste. For this purpose, in this study, the machinability of a HfTaTiVZr RHEA was evaluated with wire electric discharge machining (WEDM). The surface morphology, crack formation, and mechanical characteristics of the surface layer were investigated as a function of three different cutting conditions: rough cutting, semi-finishing, and finishing. The RHEA was precision cut in three passes by reducing the volume of material in each pass, resulting in better surface quality with the optimal cutting speed and metal removal rate. However, rough cutting gave better results than semi-finish and finished cutting processes in preserving mechanical properties.