The global escalation in emergency department patient visits poses significant challenges to efficient clinical management, particularly in clinical triage. Traditionally managed by human professionals, clinical triage is susceptible to substantial variability and high workloads. Although large language models (LLMs) demonstrate promising reasoning and understanding capabilities, directly applying them to clinical triage remains challenging due to the complex and dynamic nature of the clinical triage task. To address these issues, we introduce TriageAgent, a novel heterogeneous multi-agent framework designed to enhance collaborative decision-making in clinical triage. TriageAgent leverages LLMs for role-playing, incorporating self-confidence and early-stopping mechanisms in multi-round discussions to improve document reasoning and classification precision for triage tasks. In addition, TriageAgent employs the medical Emergency Severity Index (ESI) handbook through a retrieval-augmented generation (RAG) approach to provide precise clinical knowledge and integrates both coarse- and fine-grained ESI-level predictions in the decision-making process. Extensive experiments demonstrate that TriageAgent outperforms state-of-the-art LLM-based methods on three clinical triage test sets. Furthermore, we have released the first public benchmark dataset for clinical triage with corresponding ESI levels and human expert performance for comparison.