You can cut or break off the pups at the point where they are attached to the "mother plant". If you cut them, be sure to use a clean, sharp knife WITHOUT a serrated edge. Some of the older ones may appear shriveled or have rows of tiny holes in them. The shriveled ones have some rot. The little holes are from iris borers. Put either of these in the trash. Don't compost them. I have been known to cut off the shriveled parts, then plant the remaining part. If you do this, wash the knife very well before using it on additional rhizomes to avoid spreading disease to other plants.