Choose a cool day in spring or fall. Dig around the outside of the gaura clump with a shovel, severing roots cleanly. When you've trenched around the plant, cut underneath the plant so you can lever it from the ground. Cut deeply so you get as much of the taproot as possible.
Shake off most of the soil and wash the roots clean of any remaining soil using a garden hose.
Locate the taproot. Examine the plant and decide how to divide it, usually in clumps that are about 1/4 the size of the mother plant. Using a clean sharp knife, cut through the taproot so that each division has a piece of the taproot.
Replant the divisions in individual containers or back in the garden bed, digging a hole deep enough to contain the length of the taproot. Water the divisions thoroughly.