A method of machining a work-piece formed of titanium-based material, using a machining apparatus, is described. The method includes the steps of providing an electrically-conductive electrode contained within a spindle assembly, in a pre-selected distance and position relative to the titanium-based work-piece; while electrically powering the electrode and the work-piece with a power supply. In the process, fluid electrolyte is circulated through at least two pathways in the machining apparatus—an internal conduit within the spindle assembly; and an external conduit. The charged electrode is moved relative to the work-piece in a plunging motion, to remove material from the work-piece at a relatively high rate, using a high-speed electro-erosion (HSEE) process.