Three-dimensional (3D) point clouds are important data representations in visualization applications. The rapidly growing utility and popularity of point cloud processing strongly motivate a plethora of research activities on large-scale point cloud processing and feature extraction. In this work, we investigate point cloud resampling based on hypergraph signal processing (HGSP). We develop a novel method to extract sharp object features and reduce the data size of point cloud representation. By directly estimating hypergraph spectrum based on hypergraph stationary processing, we design a spectral kernel-based filter to capture high-dimensional interactions among point signal nodes and to better preserve object surface outlines. Experimental results validate the effectiveness of hypergraph in representing point clouds, and demonstrate the robustness of the proposed algorithm under noise.