Conventional microscopic spectral imaging suffers from extended scanning times across wavelength or spatial dimension. To improve capabilities of dynamic microscopic spectral imaging, we developed a snapshot computed tomographic microscopic imaging spectrometer (CTMIS) based on the zeroth and first orders dispersive diffraction of a two-dimensional grating. Utilizing the CTMIS-UNET reconstruction algorithm, we can reconstruct a spectral cube (541x541x26) for each frame of micro spectral imaging video. Experimental results demonstrate a sub-4 μm spatial resolution achievable through a 20x objective lens and a spectral resolution better than 10 nm among 450–700 nm, while maintaining spectral cosine similarities exceeding 0.9989 when comparing reconstructed spectra with ground truth data. Spectral imaging videos of four species of algae and mixed algae were captured under 10 ms exposure time using the CTMIS system. Leveraging the self-developed UNET-SI26 algae recognition network, precise identification and tracking of four types of algae and poisonous microcysts aeruginosa in mixed algae were conducted. The pixel-level recognition accuracy exceeds 95 %, while the accuracy for counting the numbers of different types of cells surpasses 85 %, offering an efficient and accurate spectral imaging method for real-time monitoring and early warning of harmful algae at the cellular level.