BOth ways have worked for me

I have done it at every time during the season. They are so hardy, I don't recall every losing one no matter what time I divided them. Having said that however, I would guess that the best time would be in the spring or fall.

I leave the dead stems on over winter, and let the tree leaves build up in them for protection. In early spring, I remove the mulch and stems and divide when they get a little new growth.

Of course, you could begin to root cuttings right now.

I'm with pinitz. I'm never been able to kill them no matter what I do to them, no matter what time of year. Keep them well watered and you can do whatever you like to them.

Tom brings up a good point. They are the easiest plant in the world to propagate. Shove trimmings in a hole in the ground and keep watered and by fall you will have lots more blooming mum plants.