Ask Mr. Smarty Plants

 All of the prairie grasses you name—Schizachyrium scoparium (little bluestem), Bouteloua curtipendula (sideoats grama),  Sporobolus heterolepis (prairie dropseed),  Eragrostis spectabilis (purple lovegrass),  Panicum virgatum (switchgrass) and Bouteloua gracilis (blue grama)—are warm season grasses that are either blooming or getting ready to bloom now at the beginning of summer.  If you want them to reseed your plot, you don't want to mow them now. If you are seeing a lot of tall weeds in your grasses that you want to remove and you can set your tractor/mower high enough to avoid cutting your grasses, you could mow those down. 

Frequency of mowing your prairie grasses depends on all kinds of conditions. As a general rule most Hill Country native grasses can be mowed at least once a year. However, if you want the species to drop its mature seed, then the mowing should occur after flowering and seed set and at least 1/2 the seeds have fallen from the plants. The timing of this event depends on the species. You can monitor your grasses to know when this has happened. 

The short answer then for the grasses you name—if you want your grasses to reseed—is that December through mid-February is the best time to mow to avoid losing seeds.  If you don't care whether they reseed (they are all perennials), then you could actually mow anytime.

There are two entries in our How to Articles that should be useful to you:  1) Recreating a Prairie and 2) Meadow Gardening.