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; 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.