Serverless computing promises fine-grained resource elasticity and billing, making it an attractive way to build complex applications as multi-stage workflows. Nonetheless, existing workflow orchestration ignores the heterogeneous demands of the computation and communication parts within a stage, potentially resulting in resource inefficiency on either side. In this paper, we advocate for computation-communication-separated orchestration to unleash hybrid resource (i.e., compute and network) elasticity. We present HyFaaS, a serverless workflow orchestrator that improves performance while ensuring cost efficiency. It seamlessly decouples computation and communication as a series of hybrid stages re-expressed within HyDAG, a novel workflow abstraction. HyFaaS uses a gray-box profiling model to identify their Pareto-optimal saturated configurations, and then deploys the saturated workflow to juggle communication and scaling overheads through two-level HyDAG partitioning. Along with event-driven runtime fine-tuning, HyFaaS further scales down the non-critical stages to reduce cost via branch-aware coordination. Experimental results show that HyFaaS surpasses existing solutions by 32.7%–50.4% on end-to-end latency, while lowering cost by up to 1.37×.