We investigate dynamic protection of cloud services supported by geo-distributed DCs (Geographically distributed Data Centers) under disaster scenarios which lead to failures of DC nodes and communication fibers. By assuming that the affected network region can be aware of an upcoming disaster for a certain early warning time before it is finally hit, and the corresponding service requests can be identified before they are disrupted, we utilize early warning time to achieve dynamic service protection by carrying out three methods: request rerouting, request relocation and service relocation. In particular, the first one reroutes requests to their original service providing DC nodes; the second one relocates requests to other service providing DC nodes; and the third one relocates requested services to backup DC nodes to support service requests. We first formulate an Integer Linear Program (ILP) model to maximize the number of disaster-affected requests that can be protected, and then propose a time-efficient heuristic solution. Extensive numerical results show that the proposed strategy can achieve good performance to protect service requests under disasters with early warning times.