Organ manipulator having suction member supported with freedom to move relative to its support

An organ manipulator including at least one suction member or adhesive disc mounted to a joint providing freedom of movement of the at least one suction member or adhesive disk relative to its support. A method for retracting and suspending an organ in a retracted position using suction (or adhesive force) so that the organ is free to move normally (e.g., to beat or undergo other limited-amplitude motion) in at least the vertical direction during both steps.