Dig around the perimeter of the root ball, about 8 inches away from the center of the clump. Slide a trowel beneath the root system and lift the entire clump out of the ground, severing as few roots as possible.
Brush the soil from the roots. Rinse lightly with water, if necessary, so you can see the roots clearly. Gently tease the root ball apart with your fingers to loosen it and release the soil.
Cut the roots into two or three sections with a sharp knife. Cut each section so it contains three or more stems and several large roots. Trim out and dispose of any dead roots or stems.
Plant the chrysanthemums immediately after dividing them. Plant the roots at the same depth they were at previously, with the crown of the plant where the shoots emerge from the roots just beneath the soil surface. Space the divided mums 18 to 24 inches apart in all directions.
Water the mums after replanting until the top 6 inches of soil is moist. Spread 2 inches of mulch over the soil surface to protect the roots and retain soil moisture.