A cloudlet is a small-scale cloud datacenter deployed at the network edge to support mobile applications in proximity with low latency. While an individual cloudlet operates on moderate power, cloudlet clusters are well-suited candidates for emergency demand response (EDR) scenarios due to substantial electricity consumption and job elasticity: mobile workloads in the edge often exhibit elasticity in their execution. To efficiently carry out edge EDR via cloudlet cluster control, two fundamental problems need to be addressed: how to incentivize the participation of cloudlet clusters and how to schedule and allocate workloads in each cluster to satisfy EDR requirements. We propose a two-stage control scheme, consisting of (i) an auction mechanism to motivate clusters’ voluntary energy reduction and select participants with the minimum social cost and (ii) an online task scheduling algorithm for chosen clusters to dispatch workloads to guarantee target EDR power reduction. Using the primal-dual optimization theory, we prove that our control scheme is truthful, individually rational, runs in polynomial time, and achieves near-optimal performance. Large-scale simulation studies based on real-world data also confirm the efficiency and superiority of our scheme over state-of-the-art algorithms.