With the rapid development of deep learning, its powerful capabilities make it possible to perform mechanical fault diagnosis of high-voltage circuit breakers (HVCBs). Among deep learning approaches, the convolutional neural network is widely used. However, while it can extract features effectively, it also has some limitations. Specifically, it depends on a large number of training data and only takes data information into account without considering structural information. These shortcomings lead to unused information and unsatisfactory model results. To address these shortcomings, this paper proposes AKNN-DMGCN, a novel dynamic multi-attention graph convolutional network based on an adaptively constructed graph, which can achieve high accuracy and robust mechanical fault diagnosis of HVCBs. First, a novel adaptive k-nearest neighbor (AKNN) graph construction method is proposed to construct informative graphs. The AKNN method can mine the relationship between the original data samples and utilize the data and label information. Thus, it has high fault tolerance to noise signals and can construct a structure graph with rich and accurate information, which can improve the overall model performance. Then, a dynamic multi-attention graph convolutional network (DMGCN) is applied for mechanical fault diagnosis of HVCBs. DMGCN fully utilizes structural and numerical information representing HVCB signals to perform classification. DMGCN has a dynamic multi-attention mechanism with strong expressive ability, which allows it to achieve high diagnostic accuracy. The experimental results indicate that the accuracy of AKNN-DMGCN reaches 97.22% on a balanced dataset and 95.01% on an imbalanced dataset, which demonstrates that the proposed method is effective for both balanced and imbalanced samples.