Propeller failure is a major cause of multirotor Unmanned Aerial Vehicles (UAVs) crashes. While conventional multirotor systems struggle to address this issue due to underactuation, over-actuated platforms can continue flying with appropriate fault-tolerant control (FTC). This paper presents a robust FTC controller for an over-actuated UAV platform composed of quadcopters mounted on passive joints, offering input redundancy at both the high-level vehicle control and the low-level quadcopter control of vectored thrusts. To maximize the benefits of input redundancy during propeller failure, the proposed FTC controller features a hierarchical control architecture with three key components: (i) a low-level adjustment strategy to prevent propeller-level thrust saturation; (ii) a compensation loop for mitigating introduced disturbances; (iii) a nullspace-based control allocation framework to avoid quadcopter-level thrust saturation. Through reallocating actuator inputs in both the low-level and high-level control loops, the low-level quadcopter control can be maintained with up to two failed propellers, ensuring that the whole platform remains stable and avoids crashing. The proposed controller's superior performance is thoroughly examined through simulations and real-world experiments.