Himalayan Blackberry vines root question.

I moved to a 5 acre home that was left abandoned for many years. The entire lot was vines about 10 feet tall surrounding the home.

We spent a weekend with chainsaws, gas hedge trimmers, metal weed eating it all down. Then mulched everything with a riding mower. And hauled the rest off.

But this leave a question for the roots, yes they will keep growing back but new growth will be easier to remove than the 10ft high 5acre lot of vines that previously resided.

If we just keep grass mowing the lot on a routine schedule will this kill off the roots in the long term? Wasting out root reserve energy. Even if this takes years, as grass cutting is routine.

It’s also invasive where I live with the county encouraging removal. The end goal does include more than just grass on the property, but these vines need addressed first.