The coded aperture snapshot spectral imager (CASSI) is an optical architecture that captures spectral images using compressive sensing. This system improves the sensing speed and reduces the large amount of collected data given by conventional spectral imaging systems. In several applications, it is necessary to analyze changes that occur between short periods of time. This paper first presents a sparsity analysis for spectral video signals, to obtain accurate approximations and better comply compressed sensing theory. The use of the CASSI system in compressive spectral video sensing then is proposed. The main goal of this approach is to capture the spatio-spectral information of dynamic scenes using a 2-dimensional set of projections. This application involves the use of a digital micro-mirror device that implements the traditional coded apertures used by CASSI. Simulations show that accurate reconstructions along the spatial, spectral and temporal axes are attained, with PSNR values of around 30 dB.