Asiatic Jasmine is a ground cover which, over time, can become very invasive, crowding out all other plants. While some people enjoy the low-maintenance aspects of well-established Asiatic jasmine, others see the plant as more of a weed that needs to be removed as quickly as possible. Unfortunately the waxy nature of its leaves make this plant resistant to products such as Roundup, which may leave you with few options when it comes to killing and removing this plant.
Set your mower to its lowest level and mow your Asiatic jasmine as close to ground level as possible. Bag up every bit of the jasmine that you can and throw it away or burn it.
Use a sod cutter to remove the top 3 inches of soil along with the shallow roots of the jasmine. As you cut, the jasmine roots should begin to sort of roll up. Pull the roots out frequently, then toss the rolled-up roots into the trash or burn them.
Use your spade to turn up the remaining soil, looking for more roots. Pull out every root you can find and toss them into the trash or burn them.
Spray the ground with Roundup or a similar product so that it can soak into any remaining roots.
Recheck the area in two weeks and dig up any new jasmine plants that might have escaped your first attempt to wipe them out. Do not allow any new jasmine plants to establish themselves.