Ask Mr. Smarty Plants

You probably have either  Eleocharis montevidensis (Sand spikerush) or  Eleocharis parvula (Dwarf spikerush). Both grow locally, but usually in marshes where they like to be wet in the winter but dry in the summer. Sand spikerush can withstand grazing, mowing, and drought. It is controlled in large areas by flooding for extended periods. Dwarf spikerush is also sold as a garden plant.

Since it is growing from tubers, and can also grow back from seeds in the soil, you will probably have to remove all the other plants and then dig all the tubers or even remove all the soil. Wait to see it there are tubers still sprouting from deeper in the ground, then replace your bed with new soil before replacing your plants.  (In the meantime, you would have to put them in pots and be sure you don't have the spikerush mixed in with the roots.) Then be vigilent in monitoring for new seedlings and get them out before they make tubers.

Texas A&M Agri-Service has a brochure on controlling spikerush with chemicals.  But they are treating it in a pond environment. You might be able to paint the proper dilution of contact poison on JUST the stems of the spikerush and thus kill it without exposing any other plants to the chemical. 

Good luck.  This sounds like it will be like removing nut-grass but hopefully the tubers will be large enough to find all of them easier than finding all the nuts of nut-grass is.

Eleocharis montevidensis