A tissue-removing catheter comprising: an elongate catheter body configured for insertion into a body lumen of a subject, the catheter body having opposite distal and proximal ends, a longitudinal axis (LA 1) extending between the distal and proximal ends, and an interior tissue-transport passage extending along the longitudinal axis; a cutter located generally at the distal end of the catheter body for rotation generally about the longitudinal axis (LA 1) of the catheter body, the cutter having a proximal end portion, a distal end portion, and a longitudinal axis (LA 2) extending between the proximal and distal end portions, the cutter including an annular cutting edge at the distal end portion of the cutter for removing tissue from the body lumen, an axial cavity defined by an interior surface of the cutter extending proximally from the annular cutting edge toward the proximal end portion of the cutter, 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 the tissue-transport passage of the catheter body; a screw blade extending longitudinally within the tissue-transport passage of the catheter body and being rotatable about its axis relative to the catheter body, the screw blade including an external helical thread for transporting removed tissue proximally within the tissue-transport passage as the screw blade rotates about its axis; and a cutter driveshaft, the cutter driveshaft having a distal end portion operatively coupled to the cutter for driving rotation of the cutter; the catheter being characterized in that: the screw blade defines an interior driveshaft passage extending longitudinally therein; and the cutter driveshaft extends longitudinally within the driveshaft passage of the screw blade and is rotatable about its axis relative to the screw blade. an elongate catheter body configured for insertion into a body lumen of a subject, the catheter body having opposite distal and proximal ends, a longitudinal axis (LA 1) extending between the distal and proximal ends, and an interior tissue-transport passage extending along the longitudinal axis; a cutter located generally at the distal end of the catheter body for rotation generally about the longitudinal axis (LA 1) of the catheter body, the cutter having a proximal end portion, a distal end portion, and a longitudinal axis (LA 2) extending between the proximal and distal end portions, the cutter including an annular cutting edge at the distal end portion of the cutter for removing tissue from the body lumen, an axial cavity defined by an interior surface of the cutter extending proximally from the annular cutting edge toward the proximal end portion of the cutter, 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 the tissue-transport passage of the catheter body; an annular cutting edge at the distal end portion of the cutter for removing tissue from the body lumen, an axial cavity defined by an interior surface of the cutter extending proximally from the annular cutting edge toward the proximal end portion of the cutter, 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 the tissue-transport passage of the catheter body; a screw blade extending longitudinally within the tissue-transport passage of the catheter body and being rotatable about its axis relative to the catheter body, the screw blade including an external helical thread for transporting removed tissue proximally within the tissue-transport passage as the screw blade rotates about its axis; and a cutter driveshaft, the cutter driveshaft having a distal end portion operatively coupled to the cutter for driving rotation of the cutter; the screw blade defines an interior driveshaft passage extending longitudinally therein; and the cutter driveshaft extends longitudinally within the driveshaft passage of the screw blade and is rotatable about its axis relative to the screw blade.