Magnetorheological Abrasive Flow Finishing (MRAFF) is a novel precision finishing process using smart magnetorheological polishing fluid. The said fluid can lead to a solid-liquid phase change under external magnetic field, and thus change Newtonian fluid to non-Newtonian Bingham plastic fluid. This smart behavior of MR-polishing fluid is utilized to precisely control the high normal and shear force, hence final cutting and polishing in work piece surface. However, because the MRAFF process coupled with magnetic field, thermal flow field, and multi-phase flow. The mechanism is so complicated that difficult to obtain operate parameters. Therefore, this research develops the numerical tools to analyze the characteristics of magnetorheological fluids and the finishing efficiency of abrasives, and meanwhile, investigates the cutting efficiency on curved-surface parts and the variations in magnetorheological fluids using the characteristic equations of magnetorheological fluid under different work piece materials and working parameters. The research result shows: when Reynolds number and Hartmann number are enhancement, will be helpful to the work piece cut depth increase, but surface roughness quality will drop, and mesh size increase can improve the surface roughness quality . In addition, in the research case analysis, the magnetic conductive material can obtain the greatly prediction of cutting depth, but fluid flow shear force is smaller than the material yield force . The cutting mechanism of the overall role is bad, can not achieve the desired effect of cutting. On the other hand, cutting depth is low in the polishing non-magnetic conductive material, because surface shear force rise since the velocity field distribution, by the Lorentz force action influence, cause better cutting effect of prediction. Finally, we can derive cutting depth equations and surface roughness quality equations from all of the parameter analysis in this research. The research results will be helpful that someone could blend magnetorheological fluid in further, prediction cutting depth and roughness quality of work piece surface in research matrix range.