Propeller failure is one major reason for the falling and crashing of multirotor Unmanned Aerial Vehicles (UAVs). While conventional multirotors can barely handle this issue due to underactuation, over-actuated platforms can still pursue the flight with proper fault-tolerant control (FTC). This paper investigates such a controller for one such over-actuated multirotor aerial platform composing quadcopters mounted on passive joints with input redundancy in both the high-level vehicle control and the low-level quadcopter control of vectored thrusts. To fully utilize the input redundancies of the whole platform under propeller failure, our proposed FTC controller has a hierarchical control architecture with three main components: (i) a low-level adjustment strategy to avoid propeller-level thrust saturation; (ii) a compensation loop to attenuate introduced disturbance; (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 at most two failed propellers and the whole platform can be stabilized without crashing. The proposed controller is extensively studied in both simulation and real-world experiments to demonstrate its superior performance.