Robotic surgery technique has gained admissibility in recent years. To provide ergonomic postures for the surgeon along with dexterous workspace for the Sinaflex robotic telesurgery system, a new haptic interface is introduced at the surgeon side of the robot. To analyze its performance, in this paper, the forward and inverse kinematics of the master manipulator are derived using a new geometrical approach. The workspace of the robot is derived, and its dexterity is investigated. Finally, to show the operational workspace and dexterity, the data collected during a dogs’ vasectomy robotic surgery by Sinaflex are analyzed. According to the simulation results, the workspace of the end effector is as large as 600×571×560 mm3 which is 40 times greater than the ergonomic human hand workspace. The in-vivo experiment shows that the operational surgery workspace is about 2.6% and 3.4% of the whole workspace for the left and right master manipulator, respectively. The dexterity of the robot based on the Global Conditioning Index, during simulation and experiment, for the position is 0.4557 and 0.6565, respectively. A large workspace along with its high dexterity of the master manipulator of Sinaflex robotic telesurgery system make it a good choice to fulfill robotic surgery technique requirements.