The vine is causing serious damage to your house. You should cut the vine at ground level, but don't pull on it until it has completely died and dried up. It is possible that the vine will lose its grip on the stucco as it dries. You can then use a scraper or other blade to cut the vine away from the structure. Do not pull in a way that your stucco comes loose.
If you allow the vine to continue to grow, your repair bill will ultimately involve replacement of the affected stucco siding. You may already have severe damage because water can enter where the vine has fractured the stucco. You should probably consult with a stucco contractor to see if the surface can be repaired and sealed before more damage occurs.