Dear Katarina Bediova , you could use precision sandpaper, the ones used for polishing optical pieces. Another option would be to use some polishing machine and abrasive suspensions of appropriate material and particle size and concentration in the slurry.

May be you find useful the following recent work by Zhou et al. where they used a chemomechanical polishing of SiC, testing two kind of slurries: Cr2O3 and colloidal silica, under conditions of high alkalinity of the slurry (pH=10) and a temperature around 55ºC. The best results were obtained with highly concentrated colloidal silica slurries.

Article Chemomechanical Polishing of Silicon Carbide

Hope it helps.

Dear Katarina Bediova , you could also use SinMat slurries, designed for SiC polishing. Recenctly the company was purchased by Integris. In the following link you can see it:

https://www.entegris.com/en/home/brands/sinmat.html

Hope it helps.

+1 for SinMat slurries, high removal rate and surface finish. Long track record on SiC.