Realizing the potential of low-Earth orbit (LEO)-based space-air–ground integrated networks requires mitigating challenges associated with LEO satellites, such as limited on-board resources, extended downlink (DL) coverage, temporal variability, and dynamic traffic demand. To mitigate these challenges, an efficient resource allocation (RA) system for beam-hopping can be designed. In this article, we address two practical issues in multidimensional RA for beam-hopping LEO under mixed channel conditions. First, we propose a new clustering algorithm for user equipment cell associations. Second, we decompose the RA problem into three subproblems: 1) time-frequency; 2) power; and 3) dynamic RA, and systematically address each subproblem to develop a comprehensive RA approach. We introduce a heuristic approach for time-frequency RA, achieving a good balance between performance and computational complexity. We extend the proposed algorithm to a practical dynamic RA scenario, where the channel parameters are unknown random variables throughout the next time slots, which makes the optimization problem an intrinsically stochastic problem. In addition, throughput balancing for several time slots becomes a dynamic process. Then, we use sequential convex approximations for power allocation and dynamic programming for dynamic RA. Numerical results show that the proposed algorithms outperform baseline methods in delay, capacity (the theoretical maximum data rate), and throughput (the actual data rate achieved).