Monica Milla of the Ann Arbor News recommends pruning chrysanthemums on July 4. She recommends cutting the buds off (or pruning away the top growth where buds form) to encourage more blooms and fuller plants.
SFGate suggests that gardeners continue to cut off flower buds that develop from late summer through early autumn to encourage a hardier and more uniform blooming period later into the autumn. If the chrysanthemum begins showing signs of fungal diseases, the infected portions should be removed and discarded as soon as symptoms appear.
About.com recommends against fall pruning for chrysanthemums, as the existing branches protect the plant's roots.