Since systemic herbicides are absorbed by plants (usually through foliage, sometimes through cut stumps) and moved into their roots to kill the entire plant, they are the most efficient and effective means of removing tenacious weeds like Paulownia. Glyphosate binds readily to soil, which is better at restricting any environmental contamination potential than is the case with other types of systemic ingredients. However, we realize some gardeners prefer to avoid using pesticides. In that case, the only alternative is to deny the suckers (root sprouts) light or to continually cut them down. The remaining live roots use-up stored energy reserves in order to resprout foliage, so by shading them of cutting them off to deny the plant photosynthesis, you'll eventually starve-out the remnants of the Paulownia's root system and it will die out and decay.

If desirable plants are growing between the suckers, smothering them (blocking the light with a cover like black landscape fabric, not blocking moisture from reaching the soil) won't work because this will weaken or kill the desirable plants as well. However, if turfgrass will be the only casualty, this can be replaced afterwards via seed or sod in autumn. Otherwise, you'll need to just cut-down all Paulownia sprouts as soon as you see them; allowing any to mature undetected will replenish some of the root system's energy reserves and prolong the process of eradication.

Miri

You're welcome!