While removing above-ground growth repeatedly for any weed will eventually exhaust the root system (and any other below-ground storage organs like nutlets or bulbs), how long that process takes is hard to guess...it might take weeks, months, or into next year. Be vigilant in that case about removing any new weed foliage, because the longer it remains to photosynthesize before being cut down, the more it can "recharge" root energy stores for fueling future regrowth. Each time a weed is forced to regrow, the roots/bulbs/etc. use-up some of their stored energy, and at some point it will become too depleted to regrow and the plant will die out.

To speed-up the removal process, you could consider using a systemic (root-killing) herbicide labeled for nutsedge control. (There aren't many options.) Given Montgomery County's lawn pesticide law, you wouldn't be able to use one of those targeted herbicides in a lawn, but could in a garden bed. Our Yellow Nutsedge web page mentions two active ingredients to look for (you'd only need one of them, not both) in an herbicide: halosulfuron and sulfentrazone. A non-selective (broader-spectrum) herbicide ingredient that may also work as an alternative is glyphosate, though it will damage anything the spray contacts, whereas those other two ingredients are more selective. If the plant in the photo that appears to be Creeping Thyme is too close to any nutsedge plants that you can't prevent spray drift from contacting its foliage, then you may need to resort to only manual removal around that plant to avoid herbicide exposure.

The presence of Yellow Nutsedge may indicate that the soil in areas it's infesting is too compacted or damp for turfgrass or other plants to thrive (unless the garden bed is planted with moisture-loving species, if it's a wetter area in the yard). In that case, addressing those issues by core-aerating (for lawn) or fixing drainage issues (if applicable) can help to discourage the weed from reappearing in the future.

Miri