A method of machining a work-piece formed of titanium-based material, using a machining apparatus 10, is described. The method includes the steps of providing an electrically-conductive electrode 14 contained within a spindle assembly 12, in a preselected distance and position relative to the titanium-based work-piece 16; while electrically powering the electrode and the work-piece with a power supply 22. In the process, fluid electrolyte is circulated through at least two pathways in the machining apparatus - an internal conduit 32 within the spindle assembly; and an external conduit 34. 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 highspeed electro-erosion (HSEE) process.