Water the Thymus praecox "Coccineus" plant thoroughly before dividing it. Run water at the base of the plant until the soil feels moist at a depth of 2 inches.
Dig up the entire Coccineus. Insert a trowel 2 to 3 inches deep into the soil around the plant. Work the trowel underneath the plant at an angle to lift the roots from the surrounding soil.
Set the plant on a large work surface outdoors. Shake lightly to dislodge the soil from around the roots.
Cut the Coccineus plant into equal portions, measuring at least 2 inches squared. Carefully cut through the roots with a gardening knife, allotting an equal portion of roots to each division.
Plant the Coccineus divisions directly in the garden bed under the same conditions as the parent plant, or grow them in 3-inch peat pots filled with potting soil.
Water the divisions to a depth of 1 inch once a week. Do not let the soil dry out for more than a day during the rooting process, or the plants will go into shock and die.
Keep the pot-grown divisions out of direct sunlight while they establish a vigorous root system. Plant them in the garden bed once a flush of new growth emerges at the tips of the stems.