A catheter and tissue cutting system percutaneously permits the creation of an anastomosis between a first and second anatomical structure, such as a vein and an artery. The system comprises a catheter having a main body with a lumen and tapered distal tip, configured to be moved distally into the first anatomical structure over a primary guidewire. A cutting electrode is nested in the main body, with a lumen which tracks over a secondary guidewire, and is insertable into the secondary anatomical structure. An energy supply is operative to energize the cutting electrode in order to cut a tissue wall defining the first anatomical structure.
