As long as we are talking about a fairly large tree, which if it is
covered in ivy it probably is, then you can spray roundup on the ivy
leaves without harming the tree. If it is at the base of the tree where
there are no limbs or tree leaves you should have no problem. Roundup
is absorbed in the green foliage and then travels to the plant roots and
kills the plant. I would try to keep it off the tree leaves but it
would take a tremendous amout of Roundup to harm a large oak, assuming
the trunk is many feet in diameter, not a young tree with a 6" diameter
trunk. The ivy above the cut you made will eventually die on its own.
Since the weather is now so cool it can survive quite some time cut off
from the root system. Some Roundup on the green leafy parts will hasten
it's demise. One thing you need to know about Roundup, it works best
when the plant is in its active growing season in the warmer months when
it is actively exchanging water and nutrients between the leaves and the
root system. In the late fall and winter this process can slow
dramatically as the temperatures drop and it can take a long time for
the Roundup to take effect. Once you get into freezing weather Roundup
generally works poorly if at all. In essence the tranport system in the
plant has slowed to a crawl or shutdown entirely and the leaves will not
take up the material before it gets washed off. Conversely, if you run
into protracted hot dry weather in the summer Roundup can loose it
effectiveness since most plants will try to shutdown and go dormant to
ride out the dry spell. Spring, early summer and early fall are the
best times to use Roundup type herbicides.

Rich wrote:
We have a massive oak tree in the front yard, and the ivy (English) that
covers the ground under it has grown up onto the tree. We recently bought
the house, and I'd guess this has been going on for 10 years--the ivy is at
least 25 feet up the trunk, and well-established.

I want to remove the ivy from the tree, so about 2 months ago I cut all of
the vines on the base of the tree--basically created a "clear cut" circle
about 1 foot up the trunk. cut off from the ground I expected the ivy on
the tree to cooperate by dying out, and then I'd pull the dead vines off of
the tree.

Right.

The ivy on the tree seems to be as healthy as ever. Is that a surprise?
Can it live without access to the ground? Does that mean it's getting
water/nutrients directly from the tree?

How should I go about removing/killing the ivy from the tree? I'm not
opposed to applying Roundup or something similar, if I can do so w/o
harming the tree.

Any recommendations would be appreciated.