Asiatic jasmine, or jasmine ground cover, is either a gardener's blessing or worst nightmare. Although jasmine is attractive, its ground cover spreads rapidly and aggressively, choking out other vegetation like a weed. The best way to kill it is by manually removing every part of the jasmine ground cover in the late fall season.
Mow on the lowest mower setting over the jasmine ground cover a couple of days before initiating the killing process.
Soak the entire area in water with a sprinkler or hose the day before you plan to eradicate the jasmine. This will soften the plant's roots and soil, making it easier to uproot and kill.
Start on one end of the area, firmly grasp the jasmine by the base and pull up with force, doing your best to remove all roots and runners. Immediately after pulling up the jasmine, place it in a bucket or large bin. Remove as much of the jasmine as possible.
Return to the starting point where you began to pull up the jasmine. Dig up a couple inches of soil to remove any root particles, runners or pieces of the ground cover that may have been missed. Add these fragments to the bin pile.
Rake over the entire area one more time to make sure you have removed all parts of the ground cover.
Discard or burn any jasmine pieces or place in a compost pile.