I have a few Cottonwood trees that have undermined and damaged the
driveway with their roots. There are other areas of sidewalk that the
damage is just starting.

I want to remove the trees, but unsure of the best approach.
If I cut the trees to a stump will this encourage the roots to grow
more? If I grind the stump, what about the roots under the drive,
will they die off ot try to grow more.

I was thinking of cutting the trees, then killing the stump and roots.
How should this whole thing be approached?

Thanks!