A method of creating an anastomosis includes steps of advancing a distal tip of a catheter device through a first blood vessel into a second blood vessel, while simultaneously advancing a proximal base of the device into the first vessel, contacting a wall of the first vessel with a distal blunt surface on the proximal base. A further step is to retract the distal tip so that a proximal blunt base of the distal tip contacts a wall of the second vessel, thereby capturing the two vessel walls between the blunt surfaces of the proximal base and the distal tip. A controlled pressure is applied between the two blunt surfaces to compress and stabilize the captured tissue and approximate the vessel walls. A clip is deployed through the captured tissue to hold the tissue in place during the anastomosis procedure. The anastomosis is created by applying cutting energy to the captured tissue.