Motion planning plays an important role in autonomous manipulators, especially when operating in confined spaces with various constraints. The problem is particularly challenging in unstructured and cluttered environments where there is no a priori information on the surroundings available. In this paper, a method for constrained motion planning of a hydraulically actuated manipulator is proposed within the context of laser cutting applications in nuclear decommissioning. This method enables the robot to move the end-effector to follow the surface of an inspected workpiece, based on the assumption that cutting points are generated from a 3D vision system. The algorithm works in two phases: in the first step, the ConstrainedRRT* motion planning algorithm computes a collision-free path for the manipulator to reach the initial cutting point above the surface of the target object whilst respecting robot kinematic constraints. In the second step, a laser cutting path is generated such that it satisfies the constraints imposed by the user and avoids singularities. The results indicate that the proposed method is robust against a degraded camera with 40 dB SNR under a 10 Gy/h radiation dose. The algorithm's performance is also compared against some well-known approaches in terms of planning time and computational complexity.