A polymeric, surgical clip having first and second curved leg members joined at their proximal end by a reduced thickness hinge portion and movable from an open position to a closed position for clamping a vessel between curved opposing inner surfaces which are substantially parallel when the clip is closed. The first leg member has a concave inner surface and a hook portion at its distal end curved toward the second leg member. The clip includes a sharp distal tip on the end of the hook portion and a sharp pointed penetrating member on the outer surface of the distal end of the hook portion. The distal end of the second leg has a longitudinal groove through which the sharp pointed penetrating member and then the sharp distal tip passes when the legs are closed. The second leg member further comprises a pair of sharp penetrating member attached to each side of the distal end on either side of the groove. These cooperate with the penetrating member of the first leg and sharp distal tip to cut tissue attached to the vessel to be clamped. A ligating clip applying instrument for applying the clip has a pair of handles pivoted about a hinge point and extends beyond the hinge point to form a pair of clip closing jaws equipped with means for engaging bosses located on the sides of the first and second leg members.