A new clutter reduction method which utilizes the multi-resolution and multi-directional information of the ground-penetrating radar (GPR) image is proposed. Sub-images obtained by stationary wavelet transform (SWT) or nonsubsampled counterlet transform (NSCT) are cast into a tensor structure presenting higher information compared to the spatial input data. A tensor-robust principal component analysis (TRPCA) algorithm is used for low-rank and sparse decomposition (LRSD) followed by inverse transform of the sparse tensor component to provide the clutter reduction results. The proposed methods TRPCA-SWT and TRPCA-NSCT are compared both visually and quantitatively to robust principal component analysis (RPCA) and TRPCA-bandpass filter (TRPCA-BPF), which employ the spatial raw GPR data and outputs of simple low-pass and high-pass filters respectively. Visual and quantitative results demonstrate that the clutter reduction performance increases when a higher number of scales and directions are used prior to the LRSD decomposition. Moreover, one of the proposed methods, TRPCA-NSCT, removes the background noise more efficiently due to its higher multi-resolution and multi-direction investigation capability, increasing the performance of the target detection algorithms.