I just moved into a house in Virginia which I intend to occupy for 20+
years. The lawn is relatively small, but the amount of work to cut the
grass is doubled by two sets of weeping willow roots growing on the surface.

If I cut the surface roots with a chain saw, what will happen? Do willow
trees have deeper roots that can sustain them? Will the severed roots die
and rot? I tend to think they won't because one of the trees was apparantly
cut down once already and has re-sprouted from the side of the stump.

Alternatively, is there a non-mowable ground cover which will thrive in the
semi-shade environment under a weeping willow (and displace the grass)?
Then I could completely avoid that area with the mower.

Thanks in advance for any answers or ideas you can share.

--Thundermaker$yahoo.com (Spud Demon)
The above may not (yet) represent the opinions of my employer.

Cutting the roots will encourage new growth - its like pruning branches. Willows are thirsty trees and the roots will extend 2.5 times the height of the tree - the roots of some species even spread 6 or 7 times the tree height. Use of herbicides can control root growth for 3 years or so. Good Luck!