A mechanical system for sequentially securing skin tissue preferably utilizes a tissue manipulator apparatus to approximate a portion of an interior surface of each of two pieces of living dermis tissue along a vertical interface below an exterior surface such that discrete target tissue zones are defined within the two pieces of living dermis tissue. An applicator apparatus includes a driving head portion positioned in the vertical interface and at least partially below the exterior surface and a handle portion positioned at least partially above the exterior surface. The applicator apparatus unilaterally drives a fastener through a first side of the living dermis tissue and then sequentially drives the fastener through a second side of the living dermis such that the fastener is positioned below the exterior surface and a portion of the fastener is positioned generally transverse to the vertical interface. The manipulator apparatus and the applicator apparatus can be arranged to be integral components operably connected together as part of a hand-held instrument capable of carrying and deploying fasteners.