This article investigates a class of finite-time cooperative tracking problems of heterogeneous mixed-order multiagent systems (MASs) with higher-order dynamics. Different from the previous works of heterogeneous MASs, the agents in this study are considered to have different first-, second-, or even higher-order nonlinear dynamics. It means that, according to different tasks and situations, the following agents can have nonidentical orders or different numbers of states to be synchronized, which is more general for the practical cooperative applications. The leader is a higher-order nonautonomous system and contains full state information to be synchronized for all agents with mixed-order dynamics. Accordingly, the spanning tree is defined based on the specific state rather than on the agent to guarantee that each following agent can receive adequate state information. Distributed control protocols are designed for all agents to achieve the ultimate state synchronization to the leader in finite time. The Lyapunov approach is used for the stability analysis and a practical example of mixed-order mechanical MASs verifies the effectiveness and performance of the proposed distributed control protocols.