This paper investigates automation of soft tissue compression for robot-assisted surgery. This is a fundamental task in surgery and includes interaction with a variety of tissues with unknown properties. In addition, due to sterilization and size constraints the use of contact force and position sensors are often avoided in surgical applications. We propose an Adaptive Model Predictive Control approach for execution of given tool trajectories in contact with unknown tissues in the absence of contact measurements. The Unscented Kalman Filter is employed in advance of system operation to identify the dynamics of a cable driven manipulator. These dynamics are then used to estimate contact force and position in free motion and in contact with tissue. An optimal control problem for automating tissue compression is formulated and is solved in real-time using Differential Dynamic Programming with Automatic Differentiation. The proposed methods are evaluated in experiments on an artificial tissue sample with unknown properties.