I used a shovel on bay tree suckers
I used a shovel on bay tree suckers. I pushed the mulch, and soil out of the way of the sucker, and used the shovel to slice the suckers that were emerging from the now exposed large roots. I did not try to butcher the large roots, but used the shovel to scrape/slice the suckers, as close to the now exposed root as possible, not leaving any stubble. The result was very successful, and the result lasted much longer than just hacking them off at ground level.
You need to get below the soil surface for the best result.