A medical grasping device (10) for vascular use, having an outer sheath (12), an elongate control member (50) extending an outer sheath (12) to a distal tip section (54), and a proximal control assembly (22) including an actuation section (24) joined to the elongate control member (50). Adjacent to the distal tip section (54) is a grasping portion (70, 70') that is extendable from the outer sheath (12) to create loops (74,74') for grasping a target object (T) for repositioning within the vascular system, or for removal from the patient, with loops being retractable into the outeer sheath to hold the target object against the device (10) during movement of the device. Elongate control member (50) is preferably a cannula or tube having a lumen (58) extending completely therethrough for placement over a guide wire (28) already in the patient.