How can I start my own muns?
Answers:
Tiptoe and the Doc have it right, by me. Cuttings are easy to start (we do it in the greenhouse all the time), but now is not a great time for that unless you have a greenhouse of your own. Small (6-8") pots of hardy mums are available at every garden center in the northern hemisphere right now (and cheap at many). If you plant a few of these, you'll have a good start up for next year. Then you can take your cuttings next spring. You need to pinch back hardy mums, anyway, to get the fall cushion mum that everyone loves. When they're tall enough that you can pinch off 2 or 3 nodes (joints) from the ends of the branches, you can easily root them in a sterile medium (sand, potting mix) and transplant to containers or into your garden late in the summer. If you're going to break up a big plant, it needs to be really big and very strong going into winter. At the end of winter, you can divide it with a sharp spade and make 2 or more plants to transplant. Normally, it's better to do this sort of thing in the late fall, but with mums, you'd have to be willing to sacrifice your fall color to do it. Also, in zone 5, mums can be easy to winter-kill, so fall transplanting is a little tricky.
Other answers:
winter is good
winter is good
You can take cuttings but that is a lot of work. I would break up an older plant (but not now when mums naturally start to bloom). Personally, I like to start mums from roots in the spring, or divide up plants in the spring just about the time the folliage breaks the soil surface. Right now, you can purchase small hardy mum plants at the store that are potted and either blooming or about to bloom -- that is another cost effective way to increase the colors and varieties of mums in your garden. Exchanging a few divided mum plants in the spring with a neighbor or friend also would be a cost effective way of increasing your stock. Hope this helps. Mums have a very shallow root system so be sure to water when needed. Good luck now with your mums! P.S. Some florist-type mums do overwinter but you have to experiment to see if they are hardy for your area.
You should take cuttings.. that is how mum growers do it in the greenhouse. They root very easily... simply take a cutting and put it in some soil or sand, water it, but not too much, keep the soil moist and in a week or so you should see tiny roots growing. You can also use rooting hormone, but that is not necessary. It'll make the cutting root faster.
I would not break a bigger plant apart... do the cuttings.
If you are going to start the mums in a greenhouse and grow them for a while, you can start them anytime. Depending on where you live, you may not want to plant mums outside, especially cuttings becasue they my not last through the winter. (Maybe if they were hardy mums).
So, cuttings you can do anytime.... to aswer the other part of your question, I'd need a little more info!