It depends on how much of the plant is left after mowing. If 80% of the plant is left, the plant will show no ill effects and the rootswill continue growing. At around 50%, the roots will stop growing. With less than 50% of the plant remaining, part of the root system will die off.

Only about half of the plant is above ground. The rest is in the root system. Mowing, grazing, or any other means of harvesting decreases the plant's ability to photosynthesize. Removing the top growth of the plant affects its ability to feed the roots.

This is really more of a factor with grazing than mowing, because frequency is also important. Plants can handle heavy grazing or mowing so long as they are given enough time to recover and build up their eserves before they are hit again.