Spectral imaging technology, which aims to capture images across multiple spectral channels and create a spectral data cube, has been widely utilized in various fields. However, conventional spectral imaging systems face challenges, such as slow acquisition speed and large size. The rapid development of optical metasurfaces, capable of manipulating light fields versatilely and miniaturizing optical components into ultrathin planar devices, offers a promising solution for compact hyperspectral imaging (HSI). This study proposes a compact snapshot compressive spectral imaging (SCSI) system by leveraging the spectral modulations of metasurfaces with dual-channel switchable metasurface filters and employing a deep-learning-based reconstruction algorithm. To achieve compactness, the proposed system integrates dual-channel switchable metasurface filters using twisted nematic liquid crystals (TNLCs) and anisotropic titanium dioxide (TiO2) nanostructures. These thin metasurface filters are closely attached to the image sensor, resulting in a compact system. The TNLCs possess a broadband linear polarization conversion ability, enabling the rapid switching of the incidence polarization state between x-polarization and y-polarization by applying different voltages. This polarization conversion facilitates the generation of two groups of transmittance spectra for wavelength-encoding, providing richer information for spectral data cube reconstruction compared to that of other snapshot compressive spectral imaging techniques. In addition, instead of employing classic iterative compressive sensing (CS) algorithms, an end-to-end residual neural network (ResNet) is utilized to reconstruct the spectral data cube. This neural network leverages the 2-frame snapshot measurements of orthogonal polarization channels. The proposed hyperspectral imaging technology demonstrates superior reconstruction quality and speed compared to those of the traditional compressive hyperspectral image recovery methods. As a result, it is expected that this technology will have substantial implications in various domains, including but not limited to object detection, face recognition, food safety, biomedical imaging, agriculture surveillance, and so on.