This study proposes a hierarchical composite adaptive sliding-mode control strategy to address the strong nonlinear dynamics of a hexarotor Unmanned Aerial Vehicle (UAV) and the external disturbances encountered during flight. First, within the position-control loop, a Terminal Sliding Mode Control (TSMC) is designed to guarantee finite-time convergence of the system states, thereby significantly improving the UAV’s rapid response to complex trajectories. Concurrently, an online Adaptive rates mechanism is introduced to estimate and compensate unknown disturbances and modeling uncertainties in real time, further enhancing disturbance rejection. In the attitude-control loop, a Super-twisting Sliding Mode Control (STSMC) method is employed, where an Adaptive rate law dynamically adjusts the sliding gain to prevent overestimation and high-frequency chattering, while ensuring fast convergence and smooth response. To comprehensively validate the feasibility and superiority of the proposed scheme, a representative helical trajectory-tracking experiment was conducted and systematically compared, via simulation, against conventional control methods. Experimental results demonstrate that the proposed approach achieves stable control within 0.15 s, with maximum position and attitude tracking errors of 0.05 m and 0.15°, respectively. Moreover, it exhibits enhanced robustness and adaptability to external disturbances and parameter uncertainties, effectively improving the motion-control performance of hexacopter UAVs in complex missions.