A self-propelled swabbing device and method for use in removing liquid to surface from within an installed wellbore casing. The device includes a longitudinally extending plunger sized to fit within said wellbore casing, and having an internal surface defining an internal flow passage extending longitudinally therethrough; a seal between said plunger and said wellbore casing; a valve stem including a valve operative to be shuttled between an opened position and a closed position to seal said internal flow passage, said valve stem extending longitudinally through said plunger to form a piston and sealed chamber maintained at a pressure below that desired for closing said valve; a biaser for biasing said valve in said opened position until a set pressure is reached, whereby said valve is shuttled to said closed position and flow through said internal flow passage is stopped; and a snap-closed device and a snap-open device for ensuring that said valve within said internal flow passage is either fully opened or fully closed until the set pressure is reached.