Poisonous Vine?

I was recently told that the vine covering the back of my garage is poisonous. Could it be poison sumac? It resembles the vines which cover some of the trees in the woods; the leaves of those vines turn red in the autumn. Whatever this plant is, I need to have it removed from the garage as well as from my poor trees. Unfortunately, I have no idea how one should go about killing a poisonous vine. Would cutting the vine be sufficient? Or must something be done to the roots? Poison or not, the vines have got to be removed.