1. A system for performing partial cylinder cut-off of an internal combustion engine, comprising: a rocker arm including first and second arms selectively operable jointly or independently; a rocker arm connecting unit selectively joining said first and second arms for joint operation; a separation-preventing unit interposed between the rocker arm and the rocker arm connecting unit, the separation-preventing unit preventing separation of the rocker arm from the rocker arm connecting unit; and a hydraulic pressure supply to supply and exhaust hydraulic pressure to and from the rocker arm connecting unit wherein supplied pressure activates said connecting unit for said joint operation.