Deep learning has immense potential in ensuring the safe operation of hydraulic axial piston pumps (HAPP). However, the complex operating environment and high cost of labeling have resulted in a scarcity of labeled fault samples. This paper proposes a novel method called Siamese Random Spatiotemporal Graph Convolutional Network (SRSGCN). Firstly, based on graph convolutional networks, a Random Spatiotemporal Graph (RSG) is designed to aggregate multi-sensor information at different time stamps, fully exploiting the spatiotemporal features of the original data. Secondly, the Siamese Neural Network (SNN) is improved by retaining the twin subnetwork structure and removing the similarity output part. While preserving feature extraction capabilities, it is endowed with classification ability. Based on its strong feature mining capability, SRSGCN can fully utilize the scarce sample information to improve diagnostic accuracy. Finally, a case study was conducted on our HAPP experimental platform. The experiments show that compared with other existing methods, this method has higher diagnostic accuracy and can effectively solve the problem of HAPP fault diagnosis under limited data conditions.