Once the elegant spathes have lived out their life, they shrivel and die like any other bloom. Like an aging green flower, it’s perfectly safe to cut them off and discard them if you feel they detract from the look of the overall plant. Pruning is best done with sharp clean shears. Simply trim the dead flower away at the base of the plant, leaving an inch or two of stem clear of the soil. This will prevent any decomposition from the dead stem sneaking down into the roots.