"Chrysanthemums do better if divided. After plants become mature, they form clumps of roots. The clump is called a “stool.” These stools are made up of thick, underground stems called stolons. Along these stolons will be found most of the plant’s live roots.
Most of us who grow them are familiar with these stolon-shots for they tend to form a circle of new roots around our established plants. These shoots can do your plants in if they are not controlled. Left to themselves they eventually can give you a tangled growth instead of the plentiful flower you’d rather have. So the plant must be divided, but that is all to the good since it gives you more plants to set out somewhere else. It also gives you plants for your friends to place in their gardens and makes you feel good in promoting beauty wherever you can.
The way to divide is to plant a five and six inch section of stolon—one with a healthy, green shoot and strong roots—in a newly prepared chrysanthemums bed, a flat or a pot. If potted, it can later be transferred to the garden. The experts call this a “Dutch” cutting." http://www.organicgardentips.com/how_to_grow_mums.html