Crab grass is an annual weed, but it acts like a perennial. It has what is called an indeterminate growth pattern. Most annual weeds grow until mature enough to produce seeds, then they die. They have one shot to reproduce.
Getting rid of crab grass can be difficult because it keeps growing all season, spring through fall. New plant growth, developing seed heads, and mature seeds will all be present on a plant throughout the warm seasons.
Mowing the crabgrass won’t stop it, or even slow it down. It will grow more flat, rather than upright and keep producing seeds, week after week, until you kill it or cold weather arrives. Seeds can lay dormant in the snow and reproduce again when warm weather arrives.