Mowing is necessary for a quality turfgrass. Mow frequently and at a proper height. The frequency and height of cut depend on the type of turfgrass, fertilization program and amount of rainfall.
The best rule of thumb is to mow enough that you never remove more than one-third of the leaf area per mowing. A common mistake is to allow the turf to become overgrown before mowing. This stresses the grass by removing too much of the foliage at one time.
When you mow turfgrass properly, it is not necessary to remove clippings for the health of the lawn. The only time you need to remove clippings is for the grass' sake is when they are so heavy that the uncut grass is not visible. Then remove the clippings to allow the sun to hit the grass. Clippings are an excellent source of slow-release nutrients to the turf.
More info can be found at the University of Arkansas Turf Website below.