Hyperspectral imaging (HSI) is essential across various disciplines for its capacity to capture rich spectral information. However, efficiently reconstructing hyperspectral images from compressive sensing measurements presents significant challenges. To tackle these, we adopt a divide-and-conquer strategy that capitalizes on the unique spectral and spatial characteristics of hyperspectral images. We introduce the Lightweight Separate Spectral Transformer (LSST), an innovative architecture tailored for efficient hyperspectral image reconstruction. This architecture consists of Separate Spectral Transformer Blocks (SSTB) for modeling spectral relationships and Lightweight Spatial Convolution Blocks (LSCB) for spatial processing. The SSTB employs Grouped Spectral Self-attention and a Spectrum Shuffle operation to effectively manage both local and non-local spectral relationships. Simultaneously, the LSCB utilizes depth-wise separable convolutions and strategic ordering to enhance spatial information processing. Furthermore, we implement the Focal Spectrum Loss, a novel loss weighting mechanism that dynamically adjusts during training to improve reconstruction across spectrally complex bands. Extensive testing demonstrates that our LSST achieves superior performance while requiring fewer FLOPs and parameters, underscoring its efficiency and effectiveness. The source code is available at: https://github.com/wcz1124/LSST.