I would bush hog the food plot and let it set about a week or two, the apply Glysophate (Round-Up). You should be able to find generic 40% for weell under $75/2.5 gal. Just follow the directions. I recommend mowing first to allow the Round-Up to get to the lower growing stuff well. If there are woody plants such as briars and saplings in the proposed plot area, then 2-4-D would be worth the expense. Might take two applications this summer to do the weeds in. Meanwhile have a soil test done and follow the remedy for the best resulting food plots this fall. It may be too late to try any summer crops, but might be worth the research to see if you want to spend the $$$.
Check with your local Ag. Extension service agent or your states' game department for free, good info on what does well in your area and soil type. I would suggest that you plant a mix for the deer. Down this way (SE Ala.) that works great. We plant wheat, forage oats, Elbon rye, Crimson clover and purple top turnip. Results in good food for the deer through about end of April.