While interacting with chatbots, users may elicit multiple intents in a single dialogue utterance. Instead of training a dedicated multi-intent detection model, we propose DialogUSR, a dialogue utterance splitting and reformulation task that first splits multi-intent user query into several single-intent sub-queries and then recovers all the coreferred and omitted information in the sub-queries. DialogUSR can serve as a plug-in and domain-agnostic module that empowers the multi-intent detection for the deployed chatbots with minimal efforts. We collect a high-quality naturally occurring dataset that covers 23 domains with a multi-step crowd-souring procedure. To benchmark the proposed dataset, we propose multiple action-based generative models that involve end-to-end and two-stage training, and conduct in-depth analyses on the pros and cons of the proposed baselines.