To address the high-dimensional nonconvex optimization challenges in cooperative control of unmanned aerial vehicle (UAV) swarms, this paper proposes a distributed spatiotemporal decoupled model predictive control (DSTMPC) framework that decomposes the complex spatiotemporal trajectory optimization problem into two sequential yet coordinated subproblems: spatial geometric planning and temporal scheduling. Firsty, the spatial layer employs a sequential convexification method based on iterative linearization with adaptive trust regions (ILAC) to handle nonconvex constraints such as obstacle and collision avoidance, while integrating control barrier functions (CBFs) for real-time safety. The temporal layer transforms trajectory tracking into an efficient convex optimization problem and achieves swarm synchronization through distributed consensus protocols. Then, building upon the open-loop decoupled system, a spatiotemporal coordination feedback mechanism based on a conflict state observer is designed, optimizing the closed-loop optimization circuit from the temporal to spatial layer. Simulation results demonstrate that the proposed framework achieves excellent control performance across scenarios of varying complexity: formation errors converge to within 0.37 m at steady state, and minimum obstacle clearances are maintained above 0.2 m. These results validate the effectiveness and scalability of the proposed method, providing a viable solution for efficient large-scale swarm control.