Magnetorheological–chemical-polishing tests are carried out on single-crystal silicon carbide (SiC) to study the influence of the process parameters on the polishing effect, predict the polishing results via a back propagation (BP) neural network, and construct a model of the processing parameters to predict the material removal rate (MRR) and surface quality. Magnetorheological–chemical polishing employs mechanical removal coupled with chemical action, and the synergistic effect of both actions can achieve an improved polishing effect. The results show that with increasing abrasive particle size, hydrogen peroxide concentration, workpiece rotational speed, and polishing disc rotational speed, the MRR first increases and then decreases. With an increasing abrasive concentration and carbonyl iron powder concentration, the MRR continues to increase. With an increasing machining gap, the MRR shows a continuous decrease, and the corresponding changes in surface roughness tend to decrease first and then increase. The prediction models of the MRR and surface quality are constructed via a BP neural network, and their average absolute percentage errors are less than 2%, which is important for the online monitoring of processing and process optimisation.