SummaryIn cloud datacenter network, deadline‐aware disaster evacuation transfers the endangered data out of disaster zone using limited residual network resources. Previous work has not jointly considered the selection of safe datacenter and reasonable allocation of bandwidth proportion in time‐varying postdisaster network environment. Therefore, they cannot make full use of network transmission capability. Based on our earlier work, we propose a new time‐varying disaster evacuation strategy with flexible traffic scheduling. We aim to maximize disaster evacuation capability in the disaster spread scenario. We construct a new disaster‐aware time‐expanded network model to divide time slots according to progressive disaster spread, and optimize the utilization of evacuation capability in the current disaster stage. In each time slot, we carry out two‐step optimization including safe datacenter selection and proportional bandwidth allocation. Especially, we select store‐and‐forward node to ensure the safety of evacuated data in the next time slot, and use marked evacuation routing search based on transmission requirement to improve the utilization of evacuation capability. Through extensive simulations we demonstrate that our strategy achieves better performance with higher evacuation transmission efficiency in the disaster spread scenario.