Collapsed buildings should be detected with the highest priority during earthquake emergency response, due to the associated fatality rates. Although deep learning-based damage detection using vertical aerial images can achieve high performance, as depth information cannot be obtained, it is difficult to detect collapsed buildings when their roofs are not heavily damaged. Airborne LiDAR can efficiently obtain the 3D geometries of buildings (in the form of point clouds) and thus has greater potential to detect various collapsed buildings. However, there have been few previous studies on deep learning-based damage detection using point cloud data, due to a lack of large-scale datasets. Therefore, in this paper, we aim to develop a dataset tailored to point cloud-based building damage detection, in order to investigate the potential of point cloud data in collapsed building detection. Two types of building data are created: building roof and building patch, which contains the building and its surroundings. Comprehensive experiments are conducted under various data availability scenarios (pre–post-building patch, post-building roof, and post-building patch) with varying reference data. The pre–post scenario tries to detect damage using pre-event and post-event data, whereas post-building patch and roof only use post-event data. Damage detection is implemented using both basic and modern 3D point cloud-based deep learning algorithms. To adapt a single-input network, which can only accept one building’s data for a prediction, to the pre–post (double-input) scenario, a general extension framework is proposed. Moreover, a simple visual explanation method is proposed, in order to conduct sensitivity analyses for validating the reliability of model decisions under the post-only scenario. Finally, the generalization ability of the proposed approach is tested using buildings with different architectural styles acquired by a distinct sensor. The results show that point cloud-based methods can achieve high accuracy and are robust under training data reduction. The sensitivity analysis reveals that the trained models are able to locate roof deformations precisely, but have difficulty recognizing global damage, such as that relating to the roof inclination. Additionally, it is revealed that the model decisions are overly dependent on debris-like objects when surroundings information is available, which leads to misclassifications. By training on the developed dataset, the model can achieve moderate accuracy on another dataset with different architectural styles without additional training.