In robot-assisted minimally invasive surgery, feedback as well as sensing of translational and grasping forces allows surgeons to manipulate the robots using an appropriate force. However, there have been limited reports on single instruments capable of sensing both forces (translational force and grasping force), with the exception of instruments with electronic sensors. In this study, a pneumatically driven surgical instrument capable of estimating both translational and grasping forces is developed. Our estimation method is based on the dynamics and pneumatic pressure changes of the instrument. For each force estimation, we applied a joint mechanism consisting of disks and a flexible backbone and constructed pneumatic driving systems, kinematic models, dynamic models, controller, and force estimator. We confirmed experimentally that the mean absolute error between the measured forces and the estimated translational and grasping forces is 0.2N or less for any condition. From these results, it is seen that the mechanical interference between the joint actuation mechanism and grasper actuation mechanism is negligibly small. A method for estimating both forces was proposed, and experimental results confirmed the effectiveness of the method.