An aspiration catheter includes an elastically deformable distal tip transformable between an orthogonal configuration and an oblique configuration to selectively and controllably appose the tip with thrombus or other matter to be aspirated. A core wire is slidably disposed in a core wire lumen within the catheter and is operably connected to the catheter distal tip. The core wire is controlled from the catheter proximal end to transform the distal tip between orthogonal and oblique configurations.