Robot manipulation in cluttered environments often requires complex and sequential rearrangement of multiple objects in order to achieve the desired reconfiguration of the target objects. Due to the sophisticated physical interactions involved in such scenarios, rearrangement-based manipulation is still limited to a small range of tasks and is especially vulnerable to physical uncertainties and perception noise. This paper presents a planning framework that leverages the efficiency of sampling-based planning approaches, and closes the manipulation loop by dynamically controlling the planning horizon. Our approach interleaves planning and execution to progressively approach the manipulation goal while correcting any errors or path deviations along the process. Meanwhile, our framework allows the definition of manipulation goals without requiring explicit goal configurations, enabling the robot to flexibly interact with all objects to facilitate the manipulation of the target ones. With extensive experiments both in simulation and on a real robot, we evaluate our framework on three manipulation tasks in cluttered environments: grasping, relocating, and sorting. In comparison with two baseline approaches, we show that our framework can significantly improve planning efficiency, robustness against physical uncertainties, and task success rate under limited time budgets.