The best way to kill crabgrass without using chemicals is to let it die naturally due to frost and then take measures to prevent further growth. Maintaining healthy grass and filling bare spots in the yard prevent the weed from growing back.
Wait for the frost to kill the crabgrass, and apply heavier fertilizer in the autumn. If any dead spots are visible in the yard, fill them with overseeding, particularly in the fall. Crabgrass is a shallow weed and grows quickly, so fill in bare spots as soon as possible to keep it from taking root.
Start watering the lawn less frequently but more deeply. Due to the shallowness of the weed, deep watering saturates the ground and keeps the weed from growing. Leave the lawn 3 inches high when mowing to protect the turf and discourage the growth of crabgrass. Doing this keeps the ground shaded, which prevents crabgrass seeds from germinating.
If you find crabgrass that is starting to grow, pull it from the ground, and plant corn gluten. Corn gluten is an organic weed and feed product that helps provide a natural herbicide without the need for chemicals. Plant corn gluten at the same time you fertilize the ground.