Question
The Mighty Oak is between 60 to 80 feet tall and just about 3 feet from the driveway.

Root growth has raised the driveway across about 15 feet from side to side.

Its time to repave the driveway.

Is trimming or eliminating that root possible before
paving the driveway?

Answer
If you are digging the drive up you can cut the roots off as it gets to the drive. This will not harm the tree. It more than likely will grow back so I would install a root barrier along the new drive on the tree side. These barriers are made of rubber/plastic material and are about 12-18 inches wide. i would install it along the area where the root was. This will stop the root from going under the new drive. Here is a web link to information on root barriers. You should be able to get these at a local nursery.
http://www.4specs.com/s/32/32-9452.html