Atmospheric pressure plasma polishing (APPP), as a noncontact chemical etching processing method, exhibits advantages of high efficiency, low cost, and high precision. Therefore, it can be used as an effective method to process silicon carbide. Based on the APPP gas discharge theory and tip electric field distortion effect, the effect of the APPP electrode structure on the plasma discharge stability and removal function is analyzed herein. Furthermore, the optimal electrode tip radius for APPP to process SiC is theoretically derived, finally verifying the optimal radius experimentally. After selecting the electrode, we systematically analyze the removal function characteristics of APPP in etching SiC under different processing parameters. By optimizing the electrode structure and process parameters, the pressureless sintered silicon carbide (S-Si) with a diameter of 50 mm, an initial surface profile error peak-valley value (PV) of 475.846 nm, and initial surface profile error root-mean-square (RMS) of 124.771 nm was processed. After processing for 21 min, the PV and RMS values of the S-SiC are reduced to 103.510 nm and 12.148 nm, respectively, and the RMS convergence rate is 90.26%. Experiments reveal that processing SiC using APP is more efficient than most traditional processing methods.