Native blueberries would make a fine plant in the clear portion. You can usually find them as 3 gallon plants at Home Depot in late spring. A bonus is that they often have excellent fall color.

For the mimosa, cut the plant off to expose the cambrium layer just beneath the outer bark. Apply Brush-B-Gon or something similar to the ring around the edge. If the stump resprouts, clip off the new shoots until the plant gives up (runs out of energy).

Good luck. The message board at GNPS (www.gnps.org) may also be helpful for Georgia specific questions or check out the Georgia forum here on GW: http://forums.gardenweb.com/forums/gagarden/

High strength RounUp used the way Esh mentioned above would probably work. It is supposed to be more effective to do a cut stem application of herbicide when the tree is preparing for dormancy since it sends more sap down to prepare for winter (not sure how hard your winters are however). The suggestion of blueberry shrubs sounds great and they do tend to be easy to find and purchase. I think Paw Paw trees might be nice for your area also. Those mimosas probably left some seeds behind so some follow up will probably be required. Mulch all of your plantings. Best of luck.

If you are looking for berry bushes for wildlife, I'd keep my eyes open this fall in your area. There will be wild berry bushes that are thriving in conditions just like you have on your land, and that are the right size, appearance, and generally suit your needs. Figure out what these plants are, and that will give you good ideas what to plant. Around here, Gray Dogwood, Elderberry, Blackhaw Viburnum all grow well in drier spots, while REd Osier Dogwood, Arrowwood viburnum, and Winterberry Holly are a few berry plants found in wetter spots. You'll probably have a different mix of species, but I'd try to figure out what does well in your area and grow those. it will make you life a lot easier and make you look like a good gardener without really trying.

mimosa. Hate those things. I cut the ones I find down and then in the fall I drill large diameter holes in the trunk and pour salt in the holes. It works pretty good on the smaller ones. I may try the brush b gone. I've used it on old growth Ivy before and it worked. Took a couple of applications but it got there.