An apparatus and method for delivering a vessel plug into a wound or incision in a living patient are described. The apparatus includes an expandable porous mesh mounted at the distal end of an elongate catheter. The expandable mesh may be positioned within a blood vessel or a target organ and expanded. When the mesh member is in an expanded condition, the mesh can be positioned adjacent the opening within the vessel or organ and a vessel plug can be inserted into the wound. The expanded mesh prevents the advancement of the vessel plug into the vessel or target organ, thereby avoiding possible thrombosis or stenosis within the vessel at the wound or incision site. Occlusion of the blood vessel during treatment is avoided by providing the expandable mesh with a porous construction which allows blood or other body fluids to flow therethrough while the apparatus is being used within the body of the patient. Non-thrombogenic materials can be used to treat the apparatus to prevent significant coagulation on the device during its use.