That's right. This terrible weed that you can probably find all around you right now is an extremely prolific grower. It forms a dense root network underground which makes eradicating it near-impossible without drastic and expensive interventions. Pulling it only signals it to grow more while it strangles all of the other plants in the area. It would be incredibly irresponsible of you to cut a vine into slivers with one leaf each, dig little holes around the property, and plant them. You will cause thousands of dollars of damage to the property which can't be traced back to you and that's wrong.
If this is not native to your area, please DO NOT do this.
A more effective less damaging method would be to go get some vinegar and dump it. Desiccates plants. Bio degrades/can be diluted.