In data relay satellite (DRS) systems, the performance of tasks scheduling is influenced by the variation of task and resources, which degrades the processing capacity of relay satellites. Considering this problem, we investigate the dynamic scheduling in the application of DRS. To achieve the efficient resource utilization and reliable data transfer, the strategies of task preemptive switching and decomposition are designed. Based on the initial scheme, we construct a dynamic scheduling model with multiple objectives, including maximizing the total weight of scheduled tasks, minimizing the change of scheduling scheme and minimizing the number of decomposed subtasks. Meanwhile, a preemptive dynamic scheduling algorithm (PDSA) is designed to solve the proposed model. Explicitly, our simulation results show that PDSA is superior to the whole rescheduling algorithm (WRA) in quantities of completed tasks, rescheduling rate of scheme and processing time, which can efficiently improve the performance of dynamic scheduling in DRS systems.