This work describes numerical methods for the joint reconstruction and segmentation of spectral images taken by compressive sensing coded aperture snapshot spectral imagers (CASSI). In a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation of both spectral information and 2D spatial information of a scene, resulting in significant savings in acquisition time and data storage. The double disperser coded aperture snapshot imager (DD-CASSI) is able to capture a hyperspectral image from which a highly underdetermined inverse problem is solved for the original hyperspectral cube with regularization terms such as total variation minimization. The reconstruction process decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene, and is therefore an indispensable component of the spectral imager. In this study, we seek a particular form of the compressed sensing solution that assumes spectrally homogeneous segments in the two spatial dimensions, and greatly reduces the number of unknowns. The proposed method generalizes popular active contour segmentation algorithms such as the Chan-Vese model and also enables one to jointly estimate both the segmentation membership functions and the spectral signatures of each segment. The results are illustrated on a simulated Hubble Space Satellite hyperspectral dataset, a real urban hyperspectral dataset, and a real DD-CASSI image in microscopy.