In this paper, we present visibility-based spatial reasoning techniques for real-time object manipulation in cluttered environments. When a robot is requested to manipulate an object, a collision-free path should be determined to access, grasp, and move the target object. This often requires processing of time-consuming motion planning routines, making real-time object manipulation difficult or infeasible, especially in a robot with a high DOF and/or in a highly cluttered environment. This paper places special emphasis on developing real-time motion planning, in particular, for accessing and removing an object in a cluttered workspace, as a local planner that can be integrated with a general motion planner for improved overall efficiency. In the proposed approach, the access direction of the object to grasp is determined through visibility query, and the removal direction to retrieve the object grasped by the gripper is computed using an environment map. The experimental results demonstrate that the proposed approach, when implemented by graphics hardware, is fast and robust enough to manipulate 3D objects in real-time applications.