Will it cause damage or blood clots?
Varicose veins are formed due to damaged valves of the venous system that allow pooling of the blood with resulting enlargement of the vessels. Unless you address the underlying problem (the damaged vessels), simply "draining" the vessel by aspirating blood from the varicose vein will not achieve any lasting results. You may cause damages in forms of possible infection, bruising, hematoma, pain, and clot formation (thrombosis) of the vessels. There are well established and effective treatments for varicose veins, such as Sclerotherapy, endoveous laser treatment, or possible transcutaneous (non invasive) laser treatment if vessels are small enough. Please do seek for professional help rather than contemplating sticking a needle to your veins. Best of luck.