Newly planted lawns are more delicate than established ones, and you need to be more careful when mowing them. The soil is soft and the young grass plants usually are not deeply rooted by the first mowing. The good news is that mowing encourages plants to spread and form a thicker lawn, especially when you've planted plugs or sprigs.
New lawn mowing tips:
Mow after it's grown one-third higher than regular mowing height. For example, if your grass should be maintained at 2 inches, mow it for the first time at three. It's best to remove less than one-third of the total grass height. In this example, that's one inch. Allowing the grass to grow too high before mowing it can cause undue stress to the young blades.