Providing a reliable explanation for clinical diagnosis based on the Electronic Medical Record (EMR) is fundamental to the application of Artificial Intelligence in the medical field. Current methods mostly treat the EMR as a text sequence and provide explanations based on a precise medical knowledge base, which is disease-specific and difficult to obtain for experts in reality. Therefore, we propose a counterfactual multi-granularity graph supporting facts extraction (CMGE) method to extract supporting facts from irregular EMR itself without external knowledge bases in this paper. Specifically, we first structure the sequence of EMR into a hierarchical graph network and then obtain the causal relationship between multi-granularity features and diagnosis results through counterfactual intervention on the graph. Features having the strongest causal connection with the results provide interpretive support for the diagnosis. Experimental results on real Chinese EMR of the lymphedema demonstrate that our method can diagnose four types of EMR correctly, and can provide accurate supporting facts for the results. More importantly, the results on different diseases demonstrate the robustness of our approach, which represents the potential application in the medical field.