Electrochemical jet machining (EJM) encounters significant challenges in the microstructuring of chemically inert and passivating materials because an oxide layer is easily formed on the material surface, preventing the progress of electrochemical dissolution. This research demonstrates for the first time a jet-electrolytic plasma micromachining (Jet-EPM) method to overcome this problem. Specifically, an electrolytic plasma is intentionally induced at the jet-material contact area by applying a potential high enough to surmount the surface boundary layer (such as a passive film or gas bubble) and enable material removal. Compared to traditional EJM, introducing plasma in the electrochemical jet system leads to considerable differences in machining performance due to the inclusion of plasma reactions. In this work, the implementation of Jet-EPM for fabricating microstructures in the semiconductor material 4H-SiC is demonstrated, and the machining principle and characteristics of Jet-EPM, including critical parameters and process windows, are comprehensively investigated. Theoretical modeling and experiments have elucidated the mechanisms of plasma ignition/evolution and the corresponding material removal, showing the strong potential of Jet-EPM for micromachining chemically resistant materials. The present study considerably augments the range of materials available for processing by the electrochemical jet technique.