Microgrids have the potential to withstand the power outages due to their ability of islanding and potential to sustain the penetration of renewables. Increased penetration of renewables can be beneficial but it may result in curtailment of renewables during peak generation intervals due to the limited availability of storage capacity while shedding loads during peak load intervals. This problem can be solved by adjusting the load profiles, i.e., demand response (DR) programs. In contrast to the existing studies, where DR is triggered by market price signals, a local resource-triggered survivability-oriented demand response program is proposed in this paper. The proposed DR program is triggered by renewable and load level of the microgrid with an objective to minimize the load shedding and curtailment of renewables. The uncertainties in load and renewables are realized via a robust optimization method and the worst-case scenario is considered. The performance of the proposed method is compared with two conventional operation cases, i.e., independent operation case and interconnected operation case without DR. In addition, the impact of renewable penetration level, amount of shiftable load, and load absorption capacity on the performance of the proposed method are also analyzed. Simulation results have proved the proposed method is capable of reducing load shedding, renewable curtailment, and operation cost of the network during emergencies.