A system and method for joining an end of a tubular prosthesis to the wall of a vessel wherein an anvil is inserted into the vessel through an opening in the vessel wall produced by a cutting surface on the anvil. The anvil is operated via an anvil handle which may extend through the tubular prosthesis. The tubular prosthesis is guided to the opening in the vessel wall whereupon jaws clamp the prosthesis around the anvil. Staples mounted on the jaws engage the anvil and are bent to thereby staple the end of the tubular prosthesis to the vessel wall. A cutting edge may be mounted to the anvil and utilized to create an enlarged hole to permit blood flow into the tubular prosthesis and to permit removal of the anvil from the vessel.