Adding redundant passive joints to a robotic arm is an effective way to make the robot overcome the inherent incision constraint of minimally invasive surgery (MIS). However, due to the limited motion accuracy, it is difficult to realize full-dimensional intuitive motion based on traditional multi-axis coordinated control technology in this kind of MIS robots. To solve this problem, a separated position and orientation mapping strategy for MIS robot with redundant passive joints is proposed in the paper. The position and orientation mapping of the strategy are realized by coordinate motion control and joint direct control technique, respectively. To realize the intuitive motion under this condition, an inverse motion mapping method is further proposed. Compared with the existing mapping strategy, the proposed strategy is much more compact as the orientation mapping is greatly simplified. A large number of in vivo trials based on the newly developed prototype have been conducted and results fully verify the effectiveness of the proposed strategy.