This paper is concerned with the problem of collision-free path planning for manipulators with pose constraints, such as opening a door around its pivot hinge to prevent damage. To address the inefficiency of traditional sampling-based algorithms in handling pose-constrained problems, a novel constraints elimination approach is devised to rapidly project the random sample node onto the implicit constraint manifold by converting the pose deviation into the joint angle increment, thus notably decreasing the time required to plan a feasible path. By incorporating the proposed constraints elimination approach into the previously developed algorithm, the established algorithm can efficiently compute collision-free and pose-compliant paths for manipulators in significantly reduced time. Experimental results show that the proposed approach surpasses the existing approaches in success rate and time consumption.