The introduction of autonomous mine trucks can improve the efficiency, productivity, and safety of open-pit mines, but may require more reasonable dynamic truck dispatching system to guide routes and schedules than manual driven mine trucks. In practical operations, for security consideration, only one autonomous mine truck is allowed to pass through each intersection at a time, which may lead to endogenous congestion at intersections. In this paper, we first introduce the autonomous mine trucks and endogenous congestion at intersections in the dynamic truck dispatching problem. We propose the concept of road resource which denotes the time-extended intersection and give the time–space network with road resources. The rolling horizon framework is applied to model the dynamic feature. In each horizon, the dispatching of autonomous mine trucks is formulated as a mixed integer linear programming model on the time–space network with road resources. To solve the dispatching problem in each horizon, we propose a Lagrangian relaxation algorithm to decompose the problem into a series of shortest path problem, which is solved by the designed label setting algorithm. Moreover, to yield high-quality feasible solution in each iteration of Lagrangian relaxation algorithm, a repairing algorithm with an adaptive initialization strategy is designed. A case study of an open-pit mine in China is involved to show the efficiency of the designed model with road resources and the proposed algorithm. The discussions about the productions, waiting time, travel distance, and serving time are given by sensitivity analysis.