Remove part of an umbrella sedge by simply cutting vegetation near the crown using bypass pruners. Eliminate any old or sickly looking shoots while you're trimming. Dispose of waste promptly since the tops of the umbrella sedge can root and become new plants.
Cut the sedge to the ground once every two years in locations where it is able to grow continuously. Use bypass pruners to clip the individual stalks or a lawn mower if you can reach the sedge with it -- obviously a planting in standing water needs to be trimmed by hand.
Divide the sedge using a sharp shovel when it begins to get thin in the middle. Lift the plant from its water feature or pot. Use the shovel to slice through the clumps. Replace part of the plant in the original location.