If killing them is what you want to do, then cut them off at the base with hand snips or a saw, whichever will handle the job. Paint the stump with Round-Up using a small paint brush. That will kill the stump and roots, and after some time, the stump can be easily removed, or ground and buried.

The vines themselves will take more time and effort. Getting them off the house will take some effort and care, as they have to be pulled off, and pried off where they won't simply come off with a good tug. Care must be taken in order to avoid damage to the siding. If the siding is brick, it should withstand the project. But if the siding is claps or shingles, and they're old, they may sustain damage if care is not taken. After the vines are all pulled off and disposed of, you will likely see quite a few little tendrils still attached to the house...quite a few. These are the little hands and feet with which the vines attaches itself to a surface. They will probably not come off with the vine. Getting the off will take time and effort, too. Scraping is the method usually used, with either paint scraper or wire brush, or both. But again, care must be taken so as to not unduly damage the siding.

Not an easy route, but I know of no other. Vines look nice until you want them gone...and then they lose their appeal real quick.

I appreciate your help, Thanks again.

It's best to remove them as vines hold moisture to the side of your house...could cause future problems. Had the roughest time trying to get them off our garage. Remember patience.
Good luck.