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 the 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 targets.