This paper presents a study of the grinding of three different grades of silicon carbide (SiC) under the same conditions. Surface topography is analyzed using coherent scanning interferometry and scanning electron microscopy. The study provides a baseline understanding of the process mechanics and targets effective selection of process parameters for grinding SiC optics with near optical level surface roughness, thus reducing the need for post-polishing. Samples are raster and spiral ground on conventional precision machines with metal and copper-resin bonded wheels under rough, medium, and finish grinding conditions. Material microstructure and grinding conditions affect attainable surface roughness. Local surface roughness of less than 3 nm RMS was attained in both chemical vapor deposition (CVD) and chemical vapor composite (CVC) SiC. The tool footprint is suitable for sub-aperture machining of a large freeform optics possibly without the need for surface finish correction by post-polishing. Subsurface damage will be assessed in Part 2 of this paper series.