Abstract: To address the influence of strong clutter backgrounds caused by low-speed platform motion and shallow-water reverberation on low-speed moving target detection, this paper analyzes the spatiotemporal migration characteristics of clutter in range–azimuth echograph sequences acquired by shallow-water active detection. The clutter is classified into two main types: flickering clutter, whose position and intensity vary randomly, and dynamic clutter, which exhibits relatively consistent spatiotemporal variations within a local neighborhood. Based on the classical tensor robust principal component pursuit (TRPCP), a stable tensor principal component pursuit method with tubal group sparsity enhancement (STPCP-TSE) is developed to suppress flickering clutter. Subsequently, according to the motion characteristics of the target relative to dynamic clutter, high-order spatiotemporal lacunarity (HOST-Lac) is employed to suppress dynamic clutter. Finally, the proposed method is validated using experimental data from the South China Sea. Under shallow-water clutter interference, the area under the ROC curve (AUC) of the proposed method is improved by more than 0.1 compared with the frequency-filtering tensor robust principal component analysis method, demonstrating superior detection performance.