Karst rocky desertification (KRD) is a significant issue that affects the ecological and economic sustainability of southwest China. Obtaining the accurate distribution of different levels of KRD can provide decision-making support for the effective management of KRD. The Sustainable Development Goals Science Satellite 1 (SDGSAT-1) is the world’s first scientific satellite serving the 2030 Agenda for Sustainable Development of the United Nations, and is dedicated to developing high-resolution, multi-scale, global public datasets to support policy and decision-making support systems for sustainable development. SDGSAT-1 multispectral data provide detailed ground information with a spatial resolution of 10 m and a rich spectral resolution. In this study, we combined the red-modified carbonate rock index (RCRI, an index that characterizes the degree of carbonate rock exposure) and the normalized difference red edge index (NDRE, an index that characterizes the degree of vegetation coverage) to propose a novel feature space method based on SDGSAT-1 multispectral data to classify the different levels of KRD in the Jinsha County of Guizhou Province, a representative region with significant KRD in southwest China. This method effectively identified different levels of KRD with an overall classification accuracy of 87%. This was 20% higher than that of the grading index method, indicating that SDGSAT-1 multispectral data have promising potential for KRD classification. In this study, we offer a new insight into the classification of KRD and a greater quantity of remote-sensing data to monitor KRD over a wider area and for a longer period of time, contributing to the economic development and environmental protection of KRD areas.