This paper presents a low-rank matrix completion approach to tackle the problem of wall clutter mitigation for through-wall radar imaging in the compressive sensing context. In particular, the task of wall clutter removal is reformulated as a matrix completion problem in which a low-rank matrix containing wall clutter is reconstructed from compressive measurements. The proposed model regularizes the low-rank prior of the wall-clutter matrix via the nuclear norm, casting the wall-clutter mitigation task as a nuclear-norm penalized least squares problem. To solve this optimization problem, an iterative algorithm based on proximal gradient technique is introduced. Experiments on simulated full-wave electromagnetic data are conducted under compressive sensing scenarios. The results show that the proposed matrix completion approach is very effective at suppressing unwanted wall clutter and enhancing the desired targets.