A surgical apparatus and methods for severing and welding tissue, in particular blood vessels, include a pair of relatively movable jaws at a distal end of an elongated shaft. A first heating element on one of the jaws is adapted to heat up to a first temperature and form a welded region within the tissue, while a second heating element on one of the jaws is adapted to heat up to a second temperature and sever the tissue within the welded region. A force-limiting mechanism is provided to limit the pressure applied to the tissue by the jaws to ensure that the tissue is severed and the ends effectively welded within a short amount of time.