Trim down the stalk of the tulip plant to the soil level by using pruning shears. The stalk does not have to be dead to cut. When removing the stalks, cut as close to the soil level, or base of the plant, as possible.
Cut the head of the bloomed bulb off using pruning shears. Cut about an inch down, on the stalk, from the bulb. Cutting off the dead bulbs will help preserve the plant.
Pluck leaves by hand or use pruning shears. Trimming the leaves will thin out the plant.