Accurate, real-time, and dynamic monitoring of crop planting distributions in hilly areas with complex terrain and frequent meteorological changes is highly important for agricultural production. Dual-polarization SAR has high application value in the fields of feature classification and crop distribution extraction because of its all-day all-weather operation, large mapping bandwidth, and easy data acquisition. To explore the feasibility and applicability of dual-polarization synthetic-aperture radar (SAR) data in crop monitoring, this study draws on two basic methods of dual-polarization decomposition (eigenvalue decomposition and three-component polarization decomposition) to construct time series of crop dual-polarization radar vegetation indices (RVIs), and it performs a full coverage analysis of crop distribution extraction in dryland mountainous areas of southeastern China. On the basis of the Sentinel-1 dual-polarization RVIs, the time-series classification and rapeseed distribution extraction impacts were compared using southern Hunan Province's principal rapeseed (Brassica napus L.) production area as the study area. From the comparison results, RVI3-c performed better in terms of single-point recognition capability and area extraction accuracy than the other indices did, as verified by sampling points and samples, and the OA and F-1 score of rapeseed extraction based on RVI3-c were 74.13% and 81.02%, respectively. Therefore, three-component polarization decomposition is more suitable than other methods for crop information extraction and remote sensing classification applications involving dual-polarized SAR data.