You need to make a decision, Yendor, holly or vine. The vine will eventually smother the holly and kill it but the dead tree will stay standing and provide a support for the vine for many years to come.
As the holly seems to have few leaves now then many of the branches are likely to be dead already. You could remove the vine and hard prune all the dead wood from the holly - it will keep on growing but is unlikely to look the same as it did before.

I agree with Bulbaholic...I would de-vine the tree to save if from that deadly Russian Vine!