A sparse-based refocusing methodology for multiple slow-moving targets (MTs) located inside strong clutter regions is proposed in this paper. The defocused regions of MTs in synthetic aperture radar (SAR) imagery were utilized here instead of the whole original radar data. A joint radar projection operator for the static and moving objects was formulated and employed to construct an optimization problem. The Lp norm constraint was utilized to promote the separation of MT data and the suppression of clutter. After the joint sparse imaging processing, the energy of strong static targets could be suppressed significantly in the reconstructed MT imagery. The static scene imagery could be derived simultaneously without the defocused MT. Finally, numerical simulations were used verify the validity and robustness of the proposed methodology.