A method of performing anastomosis between a graft vessel and a target vessel, each having a circumferential wall and a lumen therethrough, may include providing an anastomosis tool including a tissue effector and a fluid-driven actuator operationally connected to that tissue effector; connecting the fluid-driven actuator to an energy source; placing an end of the graft vessel in proximity to the side of the target vessel; and actuating the fluid-driven actuator to connect the end of the graft vessel to the side of the target vessel.