Recommendation for what I might do this season about root shoots from Black Locust tree invading my 1yr old raised garden bed?

Spent the better part of life last spring removing dirt, plants roots and part of a hill to build my beloved beds… and the roots found their way into my dirt. Im having some ptsd! This tree is invasive! My beds are 18+ inches deep and still they have invaded.

I get I may have to dig roots out every year or build a trench, but in the meantime, THIS SEASON, what do I do? Just cut them as deep as I can go? I am wondering if this will be encourage more growth. :( is it better to pull them above the soil to dry out? Cut the invaders and add something to the ends?

Again, this is temporary fix for this season I’m looking for. Thanks!