Extracting causal relationships from a medical case report is essential for comprehending the case, particularly its diagnostic process. Since the diagnostic process is regarded as a bottom-up inference, causal relationships in cases naturally form a multi-layered tree structure. The existing tasks, such as medical relation extraction, are insufficient for capturing the causal relationships of an entire case, as they treat all relations equally without considering the hierarchical structure inherent in the diagnostic process. Thus, we propose a novel task, Causal Tree Extraction (CTE), which receives a case report and generates a causal tree with the primary disease as the root, providing an intuitive understanding of a case's diagnostic process. Subsequently, we construct a Japanese case report CTE dataset, J-Casemap, propose a generation-based CTE method that outperforms the baseline by 20.2 points in the human evaluation, and introduce evaluation metrics that reflect clinician preferences. Further experiments also show that J-Casemap enhances the performance of solving other medical tasks, such as question answering.