Cut completely through the vines--about chest high--with pruning shears, starting at one end of the wall and working your way to the other end. This should make the removal process much easier.
Dig up the soil around the roots--then the roots themselves--using a shovel, then scoop them out of the ground. Digging out the entire vine root system will prevent them from growing back.
Loosen the lower vines by pulling them away from the siding and lifting them up and out of the ground. Pull the bulk of the vines from the siding and then cut away any clinging vines with the shears. There will probably be some stems and branches attached to the surface.
Grab the upper portion of the vines at the bottom, then pull them up and away from the siding. You'll need to use a ladder to reach those at the top. When all the vines are loose, cut away any vines and leaves still clinging to the siding, using your shears.This helps to remove any portion of the vines that have grown under the siding.
Mix 3 parts water to 1 part bleach in a bucket, add a capful of detergent, then pour the mixture into a spray bottle. Spray all remaining vines, making sure to spray underneath the siding as well to remove any vines hiding there. After 15 minutes, rinse the surface of the siding thoroughly with the hose, making sure to rinse underneath the siding, and repeat this step until all vines and stems are removed.
Pour some cooking oil into the other bucket and using a paint brush, coat the remnants with it. Allow the oil to soak into the remaining pieces for 15 minutes, then use a stiff brush to scrape them off.