Question
I live on the side of a mountain at the foothills of the Shenandoah mountains in Virginia. This acre lot is an extreme slope, and have had much difficulty cutting the grass, which was planted only to prevent erosion. It really should never have been cleared to begin with. The soil is very rocky and is mostly clay. A regular lawn-mower can't do the job, I've lost it too many times rolling down the mountain. Any suggestions on what I can do (besides moving, of course!) It takes about 10 hours to cut, because I have to do most of it with a weedwacker. I no longer have the patience for this. I was thinking of either some professional tool or perhaps ground cover? But who knows better than an expert?  Thank you kindly for your help.  

Answer
Basically three solutions:
1.) No-mow grass, 2.) Special equipment, or 3.) Plant something else.

NO MOW Grass varieties (There are others ?this site has nice pictures):
http://www.pacificsod.com/cont/nomow.html

Testimonials:
http://www.for-wild.org/download/wantnomow/wantnomow.html

How to plant it (& how to kill the existing grass)
http://prairienursery.com/pdf/nomow2003.pdf

Self-Propelled Mowers:
Choose one with adjustable speeds, so you can set your mower to move at a comfortable walking speed. A mower with a blade-brake clutch won't shut off if you let it go, so you can bend over to pick up a toy or a branch. Self-propelled mowers cost a bit more than most walk-behind mowers, ranging from $500 to about $900.

Mowing a slope without killing yourself (Radio-Controlled!):
http://www.spider-cz.com/index.php?id=&language=en

Totally re-planting with something other than lawn:
(See the PDF above on how to kill what is already there, first!) Then may I suggest some items that will need little to no maintenance, once established?br> Blackberry (or equivalents: Gooseberry, Raspberry, etc), Juniper, VA Creeper, groundcover roses (lots of varieties)

~Marc