It is difficult for multichannel maneuvering synthetic aperture radar (SAR) to achieve ground moving target 2D velocity estimation and refocusing. In this paper, a novel method based on back projection (BP) and velocity SAR (VSAR) is proposed to cope with the issues. First, the static scene is reconstructed by BP to solve the imaging problem of multichannel maneuvering SAR. Then, the static clutter is suppressed, and the range velocity is estimated via VSAR processing. As for azimuth velocity estimation and refocusing, a velocity search method based on velocity-aided BP (VA-BP) and VSAR is proposed to accomplish them. First, each azimuth velocity in the search and the estimated range velocity are used to image the moving target in a small-sized subimage space by VA-BP, i.e., matching the range history and the Doppler phase of the moving target in the image processing. Then, multiple sets of multichannel SAR subimages corresponding to different azimuth velocities are generated, and the clutter of each set of multichannel SAR subimages is also suppressed by VSAR processing. After that, the azimuth velocity is estimated by searching the clutter-suppressed subimage of the first spatial receiving channel in each set of multichannel SAR subimages with the best refocusing quality measured by the minimum entropy. Simulation results show the proposed method can reach high accuracy in moving target 2D velocity estimation and refocusing with the absolute error of 2D velocity estimation smaller than 0.1 m/s.