Described herein are atherectomy catheters, systems and methods that include a distal tip region that may be moved laterally so that its long axis is parallel with the long axis of the main catheter body axis. Displacing the distal tip region laterally out of the main catheter body axis exposes an annular blade and opens a passageway for cut tissue to enter a storage region within the catheter. The annular blade may be internally coupled to a drive shaft that rotates the blade, and thus the exposed blade edge may have the same crossing profile (OD) as the rest of the distal end region of the catheter. Also described herein are gear-driven atherectomy devices that may use a cable drive shaft to actuate the annular blade. Both push-to-cut and pull-to-cut variations are described, as are methods for cutting tissue and systems including these atherectomy catheters.