Craniotomy is an essential neurosurgical procedure to remove a section of patient's skull. In order to do this, the surgical tools need to execute a one-degree-of-freedom skull drilling followed by a two-degrees-of-freedom skull cutting. Particularly, this two-degrees-of-freedom skull cutting motion can be treated as a pivot rotation ideally. Therefore, the craniotomy tool motion is equivalent to a remote center-of-motion (RCM), which is renowned in surgical robotics. In this paper, we proposed a novel hybrid RCM mechanism for robotic craniotomy. The mechanism is made of two orthogonal parallelogram-based linkages, which make the two rotational degrees-of-freedom decoupled. We also studied the position and differential kinematics of this new architecture and analyzed its potential singular configurations. We then set the local and global kinematic performance indices for obtaining the optimal mechanism dimensions. Finally, according to the optimization result, we created a mechanical prototype to verify the motion of the designed mechanism.