A tissue-removing catheter includes a cutter having an axial cavity and an opening extending from the axial cavity through the cutter to allow tissue removed from the body lumen by the annular cutting edge to pass proximally through the opening toward a tissue-transport passage of a catheter body. A screw blade extends longitudinally within the interior passage of the catheter body includes an external helical thread for transporting removed tissue proximally within the tissue-transport passage as the screw blade rotates about its axis. A cutter driveshaft extends longitudinally within a driveshaft passage of the screw blade and is rotatable about its axis relative to the screw blade. The cutter driveshaft having a distal end portion operatively coupled to the cutter for driving rotation of the cutter.