Legal dispute mediation plays a crucial role in resolving civil disputes, yet its empirical study is limited by privacy constraints and complex multivariate interactions. To address this limitation, we present AgentMediation, the first LLM-based agent framework for simulating dispute mediation. It simulates realistic mediation processes grounded in real-world disputes and enables controlled experimentation on key variables such as disputant strategies, dispute causes, and mediator expertise. Our empirical analysis reveals patterns consistent with sociological theories, including Group Polarization and Surface-level Consensus. As a comprehensive and extensible platform, AgentMediation paves the way for deeper integration of social science and AI in legal research.