Simple. Just keep mowing it. 5 inches tall. And then shorten it to 2 inches. It does not withstand mowing...eventually. When the top cannot use photosynthesis to send needed food the roots, the roots die. You may wish to reinforce this by digging out most of the roots with a forked implement, like a Dingo or front loader. Use pruning shears or string trimmers to cut off any sprouts that escape--never let any sprout get over 6 inches tall.
Of course, you may need to wait until winter when frost kills the tops, but not the roots. Cut it down, then...get ready to mow in spring. Use your oldest blades at first.