A large-aperture silicon carbide (SiC) aspheric mirror has the advantages of being light weight and having a high specific stiffness, which is the key component of a space optical system. However, SiC has the characteristics of high hardness and multi-component, which makes it difficult to realize efficient, high-precision, and low-defect processing. To solve this problem, a novel process chain combining ultra-precision shaping based on parallel grinding, rapid polishing with central fluid supply, and magnetorheological finishing (MRF) is proposed in this paper. The key technologies include the passivation and life prediction of the wheel in SiC ultra-precision grinding (UPG), the generation and suppression mechanism of pit defects on the SiC surface, deterministic and ultra-smooth polishing by MRF, and compensation interference detection of the high-order aspheric surface by a computer-generated hologram (CGH). The verification experiment was conducted on a Ø460 mm SiC aspheric mirror, whose initial surface shape error was 4.15 μm in peak-to-valley (PV) and a root-mean-square roughness (Rq) of 44.56 nm. After conducting the proposed process chain, a surface error of RMS 7.42 nm and a Rq of 0.33 nm were successfully obtained. Moreover, the whole processing cycle is only about 216 h, which sheds light on the mass production of large-aperture silicon carbide aspheric mirrors.