Compressive Spectral Imaging (CSI) is an emerging technology that aims at reconstructing a spectral image from a limited set of two-dimensional projections. To capture these projections, CSI architectures often combine light dispersive elements with coded apertures or programmable spatial light modulators. This work introduces a novel and compact CSI architecture based on a deformable mirror and a colored-filter detector to produce compressive spatio-spectral projections without the need of a grating or prism. Alongside, we propose a tensor-based reconstruction algorithm to recover the spatial-spectral information from the compressed measurements. Experimental results on both simulated and real datasets demonstrate efficacy of the proposed acquisition architecture and the especially crafted inversion algorithms.