Rotor-stator axial clearance is critical to the safety and efficiency of major rotating machinery. However, factors such as high-speed rotation, narrow space, high temperature, and vibration present significant challenges for high-precision dynamic measurement of axial clearance. This paper proposes an axial clearance measurement method based on an all-fiber heterodyne microwave amplitude-modulated continuous wave (microwave-AMCW) system combined with an all-phase tracking algorithm, characterized by high precision, wide bandwidth, and a large measurement range. To mitigate environmental influences, a heterodyne all-fiber microwave-AMCW optical path structure is developed, and a compact dual-core fiber sensor probe is designed. The all-phase tracking algorithm is introduced to enhance dynamic precision and expand bandwidth. Additionally, what we believe to be a novel bandwidth test method based on time division multiplexing is proposed to evaluate the system's wide-bandwidth performance. The proposed system's performance is validated through simulations and experiments. The results demonstrate that the system exhibits excellent resistance to environmental interference, with a measurement range up to 24.5 mm and a static precision better than 4.5µm. Dynamic experiments further confirm the algorithm's effectiveness, achieving a precision better than 5.3µm at 100kHz bandwidth. Compared to other clearance measurement algorithms including the Hilbert transform and FFT, the proposed method reduces dynamic error by over 74%.