There is a number of ways you can virtually eliminate problem weeds in your cutting garden. One method is to plow the area, irrigate it and wait a couple of weeks allowing the weed seed to germinate and plow again. You'll have to do this a couple of times.
Another technique is similar. Cultivate your garden area, irrigate and, again, allow the weed seed to germinate and sprout. Apply Hi-Yield Killzall or Roundup to the plants. The active ingredient in both products is glyphosate which will be absorbed and kill the plant including the roots. Once again, wait a couple of weeks and apply the control to any newly sprouted weeds. Ornamental flowers, trees and shrubs may be planted 1 day after application.
When you have planted your new plants and pulled any new weeds, apply mulch to a depth of 2 to 4 inches. Besides keeping new weed populations to a minimum, mulch keeps the soil cool during the hot summer days and aids in moisture retention.