Compressed sensing techniques have been applied to through-the-wall radar imaging (TWRI) and multipolarization TWRI for fast data acquisition and enhanced target localization. The studies so far in this area have either assumed effective wall clutter removal prior to image formation or performed signal estimation, wall clutter mitigation, and image formation independently. This paper proposes a low-rank and sparse imaging model for jointly addressing the problem of wall clutter mitigation and image formation in multichannel TWRI. The proposed model exploits two important structures of throughwall radar signals: low-rank structure of the wall reflections and jointly-sparse structure among the different polarization images. The task of removing wall clutter and reconstructing multichannel images of the same scene behind-the-wall is formulated as a regularized least squares problem, where lowrank regularization is enforced for the wall components and joint-sparsity penalty is imposed on channel images. To solve the optimization problem, an iterative algorithm based on the proximal gradient technique is introduced, which simultaneously estimates the wall interferences and yields multichannel images of the indoor targets. Experiments on real and simulated radar data are conducted under full measurements and compressive sensing scenarios. The results show that the proposed model is very effective at removing unwanted wall clutter and enhancing the stationary targets, even under considerable reduction in measurements.