Mr. Smarty Plants hates to tell you this, but removing the grass on your steep lawn is going to present you with an immediate NEW problem—erosion! Grasses with their extensive fibrous root systems are ideal plants to prevent erosion on steep slopes. Although tilling is one way to get rid of the tall grass, it will leave you very susceptible to erosion uniess you get something else with extensive roots in the ground to stabilize it quickly. If you really want to get rid of your grass, solarization is a better option. Native American Seed in Junction, Texas has a very good description of how to do this. You can read about other Grass Removal Methods from Sonoma County (California) Master Gardeners.
Now for a replacement—have you considered replacing your fast-growing tall grass with a short native grass that needs very little mowing or watering? Bouteloua dactyloides (buffalograss) is a sun-loving grass native to Georgia that has varieties that grow to only 4-inches high. Another possibility is to replace the grasses with grass-like sedges. You can read Sedge Lawns for Every Landscape by John Greenlee to learn more about them. A carefully chosen sedge species has the advantage of having a maximum height of 4 to 10 inches and being evergreen. Here are two good candidates: Carex pensylvanica (Pennsylvania sedge) and Carex texensis (Texas sedge).
The following are low-growing evergreen plants that would serve well as groundcovers if you replace your grass. You should compare the required growing conditions of each of these to the characteristics of your site.