Question about non-herbicide control of grassy weed (some kind of sedge)

[UTUSN]

O.K., this picture is not the weed but closest to the tall grassy stalks I could find. *My* annoying eyesore is clumped-root at the bottom, a few spear leaves, and 4 or 5 tall skinny stalks with a head (like "jacks" of the pick-up-jacks game) full of seeds.

A few years ago I went after them by hoe, literally every single one of the danged things and RAKING up the corpses to keep the seeding of the weeds down. I knew a certain number would be re-seeded, and that happened, but less of them, and I hoed the stages and eventually had a clear yard. But the seeds are wind borne, and this year they're back with a mocking vengeance.

My specific question for Lounge botanists is this: If I use a weedeater to cut the tall stalks with seeds and RAKE, and cut when they spring up again, and cut and cut, not giving them a chance to seed, will the plants eventually die off without their seeds?

Thanks for any help. Lounge experts far surpass Google and the internets.