The development of powerful 3D scanning hardware and reconstruction algorithms has strongly promoted the generation of 3D surface reconstructions in different domains. An area of special interest for such 3D reconstructions is the cultural heritage domain, where surface reconstructions are generated to digitally preserve historical artifacts. While reconstruction quality nowadays is sufficient in many cases, the robust analysis (e.g. segmentation, matching, and classification) of reconstructed 3D data is still an open topic. In this paper, we target the automatic and interactive segmentation of high-resolution 3D surface reconstructions from the archaeological domain. To foster research in this field, we introduce a fully annotated and publicly available large-scale 3D surface dataset including high-resolution meshes, depth maps and point clouds as a novel benchmark dataset to the community. We provide baseline results for our existing random forest-based approach and for the first time investigate segmentation with convolutional neural networks (CNNs) on the data. Results show that both approaches have complementary strengths and weaknesses and that the provided dataset represents a challenge for future research.