Water the Jasmine minimus. Hand pull any weeds growing through the ground cover. To dig out weeds, press a spade 2 to 3 inches from the base and at 6 inches in depth to lift the weed's root system through the soil.
Apply pre-emergent granules in the spring over the Jasmine minimus' garden area. Use a pre-emergent herbicide that contains trifluralin. Pre-emergent herbicides that contain trifluralin prevent annual weeds from germinating. Refrain from using before sowing Jasmine minimus seeds because pre-emergent herbicides can prevent germination.
Water the Jasmine minimus. Use 1 inch of water to help the pre-emergent herbicide sink into the soil and act as a soil barrier.
Fertilize the plant with 1 lb. of slow release nitrogen fertilizer in the spring to encourage vigorous growth. Vigorous growth prevents weeds from impeding on the Jasmine minimus area. Pour the fertilizer into a drop spreader and push back and forth over the Jasmine minimus area. Water the area after applying the fertilizer.
Spray weeds growing through the Jasmine minimus with an herbicide that contains glyphosate. Herbicides that contain glyphosate kill weeds without harming the plant. For optimal results, use on a dry, wind-free day.