In gearbox systems, a composite fault diagnosis resulting from mutual interference among different components poses a significant challenge. The traditional composite fault diagnosis methods based on conventional signal analyses and feature extractions often suffer from low sensitivity to fault characteristics and difficulty in effectively identifying composite faults. On the other hand, composite fault diagnosis research via deep learning and data-driven approaches typically faces issues such as incomplete training datasets and insufficient exploration of feature correlation information, leading to an underutilization of the fault information. Therefore, this paper proposes a deep graph residual convolutional neural network (DGRCN) based on feature correlation mining for composite fault diagnosis in gearboxes. First, Pearson correlation coefficients are utilized to explore the relationships among features in the traditional feature set, transforming these relationships into a graph-structured feature set. Next, a deep graph residual convolutional network is constructed by integrating deep graph structures into a residual framework. This network globally extracts composite fault subgraph features and explores local feature correlations. Finally, the model is trained via various composite fault datasets under complex working conditions, achieving the diagnosis and identification of composite faults under the constraint of limited samples. The experimental results demonstrate that the proposed method significantly improves composite fault diagnosis accuracy, outperforming commonly used methods in this field.