While unmanned aerial vehicles (UAVs) with flexible mobility are envisioned to enhance physical layer security in wireless communications, the efficient security design that adapts to such high network dynamics is rather challenging. The conventional approaches extended from optimization perspectives are usually quite involved, especially when jointly considering factors in different scales such as deployment and transmission in UAV-related scenarios. In this paper, we address the UAV-enabled multi-user secure communications by proposing a deep graph reinforcement learning framework. Specifically, we reinterpret the security beamforming as a graph neural network (GNN) learning task, where mutual interference among users is managed through the message-passing mechanism. Then, the UAV deployment is obtained through soft actor-critic reinforcement learning, where the GNN-based security beamforming is exploited to guide the deployment strategy update. Simulation results demonstrate that the proposed approach achieves near-optimal security performance and significantly enhances the efficiency of strategy determination. Moreover, the deep graph reinforcement learning framework offers a scalable solution, adaptable to various network scenarios and configurations, establishing a robust basis for information security in UAV-enabled communications.