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Due to the high dynamics of cloud environments and the complex dependencies between microservices, it is challenging to achieve robust real-time system fault identification. This paper proposes an interpretable fault diagnosis framework tailored for microservice architecture, namely Multi-scale Learnable Transformation Graph for Fault Classification and Diagnosis(MTG_CD). Firstly, we employ multi-scale neural transformation and graph structure adjacency matrix learning to enhance data diversity while extracting temporal-structural features from system monitoring metrics Secondly, a graph convolutional network (GCN) is utilized to fuse the extracted temporal-structural features in a multi-feature modeling approach, which helps to improve the accuracy of anomaly detection. To identify the root cause of system faults, we finally conduct a coarse-grained level diagnosis and exploration after obtaining the results of classifying the fault data. 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