Ultra-precision diamond turning can deliver very accurate form, often less than 100nm P-V. A possible manufacturing method for thin Wolter type-1 mirrors in hard X-ray space telescopes thus involves generating electroless nickel plated mandrels by diamond turning, before coating them with a reflective film and substrate. However, the surface texture after turning falls far short from the requirements of X-ray and EUV applications. The machining marks need to be removed, with hand polishing still widely employed. There is thus a compelling need for automated finishing of turned dies. A two step finishing method is presented that combines fluid jet and precessed bonnet polishing on a common 7- axis CNC platform. This method is capable of finishing diamond turned electroless nickel plated dies down to 0.28nm rms roughness, while deterministically improving form error down to 30nm P-V. The fluid jet polishing process, which consists of pressurizing water and abrasive particles for delivery through a nozzle, has been specially optimized with a newly designed slurry delivery unit and computer simulations, to remove diamond turning marks without introducing another waviness signature. The precessed bonnet polishing method, which consists of an inflated membrane rotated at an angle from the local normal to the surface and controlled by geometrical position relative to the work-piece, is subsequently employed with a novel control algorithm to deliver scratch-free surface roughness down to 0.28 nm rms. The combination of these two deterministic processes to finish aspheric and freeform dies promises to unlock new frontiers in X-ray and EUV optics fabrication.