Surgical instruments and cartridges for cutting and fastening tissues and organs such as vessels are disclosed. In various non-limiting forms, the surgical instrument includes a first jaw that operably supports a substantially flexible elongated tissue closure assembly therein. A second jaw is movably supported relative to the first jaw and is selectively movable between open and closed positions in response to opening and closing motions applied thereto. A closure retraction assembly is configured to selectively apply cinching motions to the substantially flexible elongated tissue closure assembly.