Ultra-low thermal expansion ceramics NEXCERATM is regarded as one of potential candidate materials crucial for ultralightweight and thermally-stable optical mirrors for space telescopes which are used in future optical missions satisfying extremely high observation specifications. To realize the high precision NEXCERA mirrors for space telescopes, it is important to develop a deterministic aspheric shape polishing and a precise figure correction polishing method for the NEXCERA. Magnetorheological finishing (MRF) was tested to the NEXCERA aspheric mirror from best fit sphere shape, because the MRF technology is regarded as the best suited process for a precise figure correction of the ultralightweight mirror with thin sheet due to its advantage of low normal force polishing. As using the best combination of material and MR fluid, the MRF was performed high precision figure correction and to induce a hyperbolic shape from a conventionally polished 100mm diameter sphere, and achieved the sufficient high figure accuracy and the high quality surface roughness. In order to apply the NEXCERA to a large scale space mirror, for the next step, a middle size solid mirror, 250 mm diameter concave parabola, was machined. It was roughly ground in the parabolic shape, and was lapped and polished by a computer-controlled polishing machine using sub-aperture polishing tools. It resulted in the smooth surface of 0.6 nm RMS and the figure accuracy of ~ λ/4, being enough as pre-MRF surface. A further study of the NEXCERA space mirrors should be proceeded as a figure correction using the MRF to lightweight mirror with thin mirror sheet.