You certainly can, you can even take leaf tip cutting with about three inches of stem, these are winter growers, liking cool air.
They will go dormant when it gets hot much like a chrymum, and will need to be trimmed back after they flower. I grew these for a while, but it was just tooooooo hot for them where I live. The last time I looked there where four different colors, each had it's own cv. name. Norma

Hmm. I'm not too far from Wisconsin. I divided my "Autumn Joy" this spring into 3 plants and the new plants are doing fine. I think there is some rule about dividing plants in the opposite time that they flower. So fall blooming = spring dividing.

On the other hand, I think these plants are extremely strong, so maybe it won't matter. :D

Spring dividing suits me just fine, as I am madly trying to transplant as many daylilies as I can before the middle of September. (After that, you can do it, but I've found it kind of ''iffy" here in Wisconsin.) I also appreciate dividing a smaller plant, or in other words, one that is just emerging versus something fully grown and huge. So I'll just put it on my spring calendar of "things to do"! I just didn't know if you divided them, cut them back, or what. Thanks so much! MacThayer

The telephium type sedums, like 'Autumn Joy' and its relatives, are usually considered perennials, and are treated as such. That means they should definitely be cut down - as in, right to the ground - every winter, once you've enjoyed their autumn seed heads for a while. Of course, that is also the ideal time to divide them.
The flopping issue is a different question altogether; that can only be remedied by growing them "harder" and in more sun so they don't get so lanky, and/or using a perennial ring or staking them.

Since you're in zone 4, you needn't worry about cutting back your sedum -- they'll die back to the ground after the frosts set in leaving only the seedheads (which I leave on for the winter interest). In the spring they'll jump right back up. You can divide them at any time -- even when they're in flower...just get them well-rooted before frost. They're quite adapatable and easy-going -- these are not delicate by any stretch and actually do best in areas with real winters. Plant several together and you won't need to worry about staking -- they'll hold each other up.

Thanks for all of the advice! If I can still get them divided this fall, I will (it's just that I have so much on my 'gardening plate' as it is!). But spring for sure. They were not 'flopping' until this year, and this is also the year they've grown so large. Both are in full sun positions, so I know lack of adequate sun isn't the problem. It's just that they've gotten too big! Still, it's really nice to know that I can get out there and divide them yet this fall if I have a spare moment (and take something off my spring plate of 'things to do'!) Thanks so much! MacThayer

I just realized, Patrick, that I don't know what you mean by growing my sedum "harder". Can you, or anyone, explain?
MacThayer

I prevent sedum flopping by cutting them back by half in late May (I’m in zone 5). This delays flowering by a couple weeks, but makes for huge round mounds of flowers, no flopping, no open centers.