Robotic-assisted lumbar puncture (LP) has the potential of increasing the insertion accuracy in comparison with manual operation. Remote center of motion (RCM) mechanism is the key structural components of the LP robot, which makes the needle towards the insertion point by its structural constraint. However, clinical concerns of the LP, including the patient movement, respiration, and the compliance with the physician, are not well concerned. These concerns are important in designing a LP-specialized robot for real-world application. In this work, a spherical scissor-like RCM mechanism specialized for LP is proposed. The proposed RCM mechanism is patient-mounted to reduce the influence of patient movement and respiration. With the advantages of high stiffness and compactness, spherical scissor-like mechanism is introduced and parallel connected to achieve the RCM pattern. Forward kinematics of the RCM mechanism is established based on the Denavit–Hartenberg (D-H) convention to obtain the workspace. Then, finite element simulation is performed to validate the stiffness of the proposed RCM mechanism. Finally, experiments are carried out to validate the workspace and the accuracy of the RCM point. The results show that the workspace and accuracy (1.97 mm) of the proposed RCM mechanism satisfy the requirement of the LP procedure.