Also, it is often helpful to tie foliage together before cutting so it doesn't interfere and is easier to dispose of. Burning is another option — but only if it is safe and legal to do so. Note that these grasses may not burn long, but they burn extremely hot. Even so, the crown of the plant is not damaged and new growth appears relatively quickly.
If the center of the clump shows little growth, the plant would benefit from division. Dig up the entire clump and separate. Then, replant the vigorous growth found on the outer edge of the clump. (Ward Upham)