In the context of smart cities, autonomous vehicles, such as unmanned delivery vehicles and taxis are gradually gaining acceptance. However, their application scenarios remain significantly fragmented. Typically, an Autonomous Multi-Functional Vehicle (AMFV) is not engaged in other scenarios when idle in a specific one. Currently, a unified system capable of coordinating and using these resources efficiently is lacking. Moreover, there is an absence of an advanced navigation algorithm for facilitating coordinated navigation among Heterogeneous Vehicles (HVs). To address these issues, we propose the LLM-driven Multi-vehicle Dispatching and navigation (LiMeda) framework. It comprises an LLM-driven scheduling module that facilitates efficient allocation considering task scenarios and vehicle information, which addresses the issue of incompatible vehicle resources across various smart city scenarios. And the other is a navigation module, founded on the Heterogeneous Agent Reinforcement Learning (HARL) framework we previously proposed, which can effectively perform cooperative navigation tasks among heterogeneous agents, assisting the cooperative task completion by HVs in a smart city. Experimental results show our method outperforms both traditional scheduling algorithms and Reinforcement Learning navigation algorithms in metric terms. Additionally, it shows remarkable scalability and generalization under varying city scales, vehicle numbers, and task numbers.