Certified GKH Gardening Expert
You do not want to cut anything but the flowering stalk after blooming until after the entire plant has died for the year. Cutting off anything more than the flowering stalk ONLY while it is actively growing will stunt the plant, and likely cause it to skip a year in flowering.
Once the bloom head has died remove, only, that stalk to avoid spending energy on reproduction and seed.
Here are some articles that will help: