Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs). Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a self-representation matrix with complexity of O(n^2), followed by spectral clustering. However, these methods are computationally intensive, generally incorporating solely either local or non-local spatial structure constraints, and their structural constraints fall short of effectively supervising the entire clustering process. We propose a scalable, context-preserving deep clustering method based on basis representation, which jointly captures local and non-local structures for efficient HSI clustering. To preserve local structure (i.e., spatial continuity within subspaces), we introduce a spatial smoothness constraint that aligns clustering predictions with their spatially filtered versions. For non-local structure (i.e., spectral continuity), we employ a mini-cluster-based scheme that refines predictions at the group level, encouraging spectrally similar pixels to belong to the same subspace. Notably, these two constraints are jointly optimized to reinforce each other. Specifically, our model is designed as an one-stage approach in which the structural constraints are applied to the entire clustering process. The time and space complexity of our method is O(n), making it applicable to large-scale HSI data. Experiments on real-world datasets show that our method outperforms state-of-the-art techniques. Our code is available at: https://github.com/lxlscut/SCDSC