A method for closing an opening at a target site including bodily tissue including embedding a plurality of self-closing clips into the target site in a spaced apart manner about a perimeter of the opening. Each of the clips has opposing clip ends and an intermediate segment. A flexible tether is coupled to the embedded clips to form a loop about the opening perimeter. A pulling force is applied onto at least one of the loop ends, thereby drawing the perimeter of the opening onto itself to completely close the opening. The loop ends are secured to maintain the target site in a closed state. In some embodiments, the target site is apical cardiac tissue, and the method is performed as part of a trans-apical access procedure.