Prepare soil where new plants will go in spring. Mums need well-drained soil but they do best in fertile soil. Spread 2 to 3 inches of well-rotted manure, shredded leaves and compost. Dig in organic matter and thoroughly mix it into the top 6 inches of soil to improve both drainage and fertility.
Dig, divide and replant a large, overgrown chrysanthemum clump about 3 or 4 weeks after the last killing frost in spring, when substantial new growth is apparent. Dig up the entire clump using a sharp garden spade, working your way around the outside of the clump and then popping it up from below.
Cut the clump into wedges -- like you'd slice a pie -- using the spade to make four, six or eight new plants, depending on the size of your starting bush. Slice off the tip of each wedge, the older, tired part of the plant, and discard it.
Replant mum wedges where they will grow in the garden, spacing them 18 to 24 inches apart depending on how large the new clump will grow. Be sure to plant them at the same depth they were previously. Water new mum plants thoroughly at planting and continue to water them weekly through summer and fall, in the absence of rains.
Fertilize chrysanthemums with low-nitrogen granular fertilizers such as 5-10-5, 5-10-10 or 5-20-20, either inorganic or organic. Work organic fertilizers into the soil at planting, because they take longer to release their nutrients. Fertilize mums monthly through mid-July to encourage vigorous growth.