Extracting features from point sets is becoming increasingly important for purposes like model classification, matching, and exploration. We introduce a technique for segmenting a point-sampled surface into distinct features without explicit construction of a mesh or other surface representation. Our approach achieves computational efficiency through a three-phase segmentation process. The first phase of the process uses a topological approach to define features and coarsens the input, resulting in a set of supernodes, each one representing a collection of input points. A graph cut is employed in the second phase to bisect the set of supernodes. Similarity between supernodes is computed as a weighted combination of geodesic distances and connectivity. Repeated application of the graph cut results in a hierarchical segmentation of the point input. In the last phase, a segmentation of the original point set is constructed by refining the segmentation of the supernodes based on their associated feature sizes.We apply our segmentation algorithm on laser-scanned models to evaluate its ability to capture geometric features in complex data sets.