Recently, Mamba based on State Space Models (SSMs) has shown great potential for hyperspectral image (HSI) classification due to its long-range modeling capability and linear complexity. However, existing Mamba-based methods usually employ fixed and limited scanning directions, restricting anisotropic spatial modeling. Moreover, full-pixel scanning introduces substantial computational redundancy. To address these issues, this paper proposes DESDA-Mamba, a direction-adaptive Mamba network with diagonal-enabled strided scanning for HSI classification. Specifically, a lightweight direction adaptation module is designed to implicitly predict suitable scanning directions from learned direction-sensitive feature-channel responses and perform batch-level unified direction aggregation, revealing that finer patch-level direction routing does not necessarily improve performance. In addition, a strided scanning strategy is introduced to skip redundant adjacent pixels during sequence serialization, reducing computational cost while enlarging the effective receptive field. Furthermore, two diagonal scanning modes, namely main-diagonal and anti-diagonal scanning, are proposed to improve the modeling of oblique spatial structures. Efficient diagonal scanning is implemented through coordinate-sequence indexing and caching mechanisms, enabling flexible diagonal strided scanning. Extensive comparison, ablation, and model-variant experiments on four public HSI datasets demonstrate that DESDA-Mamba achieves superior classification performance with competitive efficiency. The source code is available at https://github.com/ll-netizen/DESDA-MAMBA.