Methods and apparatuses for closure of vascular punctures or other openings in bodily tissues. The apparatuses and methods described herein are configured for everting a portion of tissue around a puncture site for wound closure on the external surface of the wound. For example, the tissue eversion apparatus may be configured for drawing up a portion of a vessel surrounding a venous or arterial puncture and orienting the inner surface of the vessel at least partially outward so that a closure element may be placed around the inverted region on the exterior surface of the vessel. In some embodiments, the devices are bioabsorbable.