A device for withdrawing a tubular body part such as a varicose vein is provided. A needle is inserted through a skin. The needle contains therein an engaging element in an undeployed state. After the needle is inserted, the engaging element is pushed out of the needle and is typically deployed inside the vein. The vein is now ready to be withdrawn by the deployed engaging element. Using a puncture device that also contains a deployable engaging element allows the puncture site to be small and causes less trauma to the surrounding tissue.