The invention discloses a magneto-rheological damper with controllable damping and negative stiffness. The magneto-rheological damper comprises a cylinder barrel assembly, a rotating piston and a ballscrew pair, wherein the rotating piston is rotationally arranged in the cylinder barrel assembly in a single-degree-of-freedom mode, and the ball screw pair is matched with the rotating piston; the cylinder barrel assembly comprises an inner cylinder barrel and an outer cylinder barrel, wherein the inner cylinder barrel rotationally sleeves the rotary piston, the outer cylinder barrel rotationally sleeves the inner cylinder barrel, the rotating piston and the inner cylinder barrel are arranged at intervals in the radial direction, a first magnetorheological fluid cavity is formed, the inner cylinder barrel and the outer cylinder barrel are arranged at intervals in the radial direction, and a second magnetorheological fluid cavity is formed. The magnitude of the current input to the exciting coils on the rotating piston and the outer cylinder barrel is controlled, so that shearing yield force of magnetorheological fluid in the first magnetorheological fluid cavity and the second magnetorheological fluid cavity can be changed, the rotating state of the inner cylinder barrel is further influenced, the controllable damping force is achieved, and the characteristic of controllable negative rigidity of the damper is realized by utilizing the moment of inertia, the controllable damping and the rigidity is realized, and the control effect of a reduction/isolation vibration system.