How large a clump are you trying to separate?

kay

you could try using two pitchforks to lever/pull them apart.
but some of the more experienced growers on here may have a better suggestion.

but i am actually really rough with mine and dont even bother trying not to hurt them, just shovel straight through them, tear into them, even throw them on the ground and let the clumps fall apart. ive learned that they are really hardy and can handle taking a beating.

though, some of these guys may publicly scorn me for it. haha! i dont suggest you do this, im just letting you know that i do it, and that most plants are not as fragile as we would expect them to be.

Cut back the foliage to 6-8" or so, so you can see what you are doing (and flopping foliage doesn't get in the way).

Dig the clump. Shake as much dirt off as you can, and then wash as much of the remaining dirt off as you can. (It helps if you can soak the clump overnight, and then blast it with the hose.)

Take two large, long, strong screwdrivers, thrust them into the center of the clump, and use them kind of like crowbars to pry the clump apart. Repeat this to pry the half clumps into smaller pieces, until you are satisfied with the size of the resultant clumps.

I learned the screwdriver trick as a newbie, watching the folks at the local daylily club divide up plants for a sale. Unless the clump is very tight, this usually works very well. Sometimes, though (especially if the clump is tight, as with some spiders) you will break off a fan or two at the crown, so it is best to just expect some attrition.

Good luck!