The development of wire electrochemical spark machining setup is always challenging in the form of industrial viable for machining advanced engineering materials such as polymer nanocomposites, quartz, glass, ceramics, etc. Because of some drawbacks associated with it, like irregularity in kerf width, poor surface finish, no spark formed at high wire velocity, wire breaking at high voltage, etc. In the present work, a newly developed hybrid machining process that is reversible motion-wire electrochemical spark machining (RM-WECSM) has been developed for curve profile cutting, especially on non-conducting workpieces such as aluminum oxide epoxy nanocomposite of 3.5 mm thickness. The effect of NaOH concentration, applied voltage, reversible wire velocity, pulse on-and-off time, on material removal rate and average surface roughness have been studied using a one-parameter-at-a-time approach. Sparking occurred from the electrolyte surface to 10 mm above the electrolyte surface to cut the workpiece. The spark length is equal to the workpiece thickness. A continuous, stable spark has been formed at a high reversible wire velocity (19.8 m/min). Simultaneously, self-electrolyte flow has been generated, due to which melted materials have been washed out of the cut-surface and provided the smooth (1.987 µm) cut-surface of the workpiece. The maximum MRR is found as 1.63 mg/min. Thermal cracks, heat-affected zones and recast layers were not found on the curve cut-surface, and it was analyzed by a field emission scanning electron microscope.