A sealing clip for sealing or holding punctures or openings in tissue closed is applied from the inner surface of the tissue. In one embodiment, the clip has piercing members for penetrating the tissue from an inner surface thereof adjacent the opening. A delivery apparatus is used to releasably hold the clip in one configuration for introduction of the clip through the puncture or opening and expand the clip to a more open configuration for pulling the clip through the tissue as the delivery apparatus is retracted. Further retraction of the delivery apparatus causes the edges of the tissue surrounding the opening to move along the clip and come together after which the clip is released and closed to hold the tissue edges of the opening together. In the case where the clip has a memory set closed shape, the clip returns toward that shape after being released to hold the tissue edges of the opening together, thereby holding the opening closed.