One of the main challenges in through-the-wall radar imaging (TWRI) is the strong exterior wall returns, which tend to obscure indoor stationary targets, rendering target detection and classification difficult, if not impossible. In this paper, an effective wall clutter mitigation approach is proposed for TWRI that does not require knowledge of the background scene nor does it rely on accurate modeling and estimation of wall parameters. The proposed approach is based on the relative strength of the exterior wall returns compared to behind-wall targets. It applies singular value decomposition to the data matrix constructed from the space-frequency measurements to identify the wall subspace. Orthogonal subspace projection is performed to remove the wall electromagnetic signature from the radar signals. Furthermore, this paper provides an analysis of the wall and target subspace characteristics, demonstrating that both wall and target subspaces can be multidimensional. While the wall subspace depends on the wall type and building material, the target subspace depends on the location of the target, the number of targets in the scene, and the size of the target. Experimental results using simulated and real data demonstrate the effectiveness of the subspace projection method in mitigating wall clutter while preserving the target image. It is shown that the performance of the proposed approach, in terms of the improvement factor of the target-to-clutter ratio, is better than existing approaches and is comparable to that of background subtraction, which requires knowledge of a reference background scene.