That plant is not easy to kill. One option is to hand dig but you can imagine how much of a chore that would be. Another is to mow it down close and then when it starts to regrow spray it with a herbicide containing glyphosate (such as Roundup) or triclopyr (such as Brush B Gon or a poison ivy killer). Use a strong solution of the glyphosate if you choose that product. The new growth is less waxy and takes up herbicides more readily than older leaves do. TAKE EXTRA CARE TO JUST BARELY WET THE JASMINE FOLIAGE...DON'T OVERAPPLY IT! If you get these products on sprouts from nearby trees or if they are overapplied and wash into the soil you can severely damage trees, shrub, flowers and other desirable plants.
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