Off-axis parabolic parts (OAPs) or quasi-OAPs are mostly frequently used in large optical telescopes. Compared to the stressed mirror polishing, computer-controlled optical surfacing (CCOS) or other computer-controlled subaperture tools provide more flexibility. However, the fabrication efficiency needs to be promoted in tactical ways. In this paper, we present a large aperture CCOS lap equipped with a compound motion unit and go through the grinding and pre-polishing with its figure errors. A CCOS-based heterocercal tool is first used in large optics to restrain the edge effects. In the fine polishing stage, corrective polishing, smoothing, and ion beam figuring are applied in combination to finish. We experimentally test this strategy on an Ø1.5 m OAP, as a part of giant steerable science mirror (GSSM) in the Thirty Meter Telescope. Finally, the surface error of Ø1.5 m OAP is better than 1/50λ RMS (full aperture), and the mid-spatial frequency part is better than 0.64 μrad in slope RMS (effective aperture). The effective fabrication duration is reduced to 2 months.