Siberians are indestructible, I think, or at least practically so. I have divided them in spring, before active growth begins; right after flowering (coming up shortly here, as they are peaking now, see photo), and also in early fall. I suppose a lot of books say right after flowering, but tackle this whenever you can (just not late fall or in the high, dry heat of midsummer, though the things would probably recover). You first dig them out, which may take a combination of shovel/spade and fork, and even more serious weaponry. You pry or cut them apart, discarding the weak or woody center portion. Some people drive two spading forks back-to-back into the center of the clump once it’s out of the ground, then work the handles to do the prying down below. Repeat. I have to admit I have also just jumped on my sharpest spade and butchered the clumps into smaller sections, when they just wouldn’t come apart any other way. Replant the new sections (roughly like wedges of a bundt cake since your center dead stuff was cut out). Depending on how big the clump was, you may get 4 or 6 or 8 or more vigorous clumps from it. I don’t chop irises into tiny bits because they’re most beautiful in masses, so I want that look again pretty quick.