The bug triaging process, an essential process of assigning bug reports to the most appropriate developers, is related closely to the quality and costs of software development. As manual bug assignment is a labor-intensive task, especially for large-scale software projects, many machine-learning-based approaches have been proposed to automatically triage bug reports. Although developer collaboration networks (DCNs) are dynamic and evolving in the real-world, most automated bug triaging approaches focus on static tossing graphs at a single time slice. Also, none of the previous studies consider periodic interactions among developers. To address the problems mentioned above, in this article, we propose a novel spatial-temporal dynamic graph neural network (ST-DGNN) framework, including a joint random walk (JRWalk) mechanism and a graph recurrent convolutional neural network (GRCNN) model. In particular, JRWalk aims to sample local topological structures in a graph with two sampling strategies by considering both node importance and edge importance. GRCNN has three components with the same structure, i.e., hourly-periodic, daily-periodic, and weekly-periodic components, to learn the spatial-temporal features of dynamic DCNs. We evaluated our approach's effectiveness by comparing it with several state-of-the-art graph representation learning methods in two domain-specific tasks that belong to node classification. In the two tasks, experiments on two real-world, large-scale developer collaboration networks collected from the Eclipse and Mozilla projects indicate that the proposed approach outperforms all the baseline methods.