Plants that have taproots can be divided by using a sharp knife to slice down the length of the root. Every piece that has at least one eye, some of the taproot, and a few side roots is a viable division.
Plants that have taproots include balloon flowers (Platycodon grandiflorus and cvs., Z 4–9), butterfly weeds (Asclepias tuberosa and cvs., Z 4–9), cushion spurges (Euphorbia polychroma and cvs., Z 4–9), Oriental poppies (Papaver orientale and cvs., Z 4–9)
In this video, author and instructor Janet Macunovich demonstrates how to divide perennials that have taproots.
Introduction to Dividing Perennials
Dividing Plants with Roots That Form Offsets
Dividing Plants with Surface Roots
Dividing Plants with Underground Running Roots
Dividing Plants with Woody Roots
10 Tips on Dividing Perennials