The flowers don't require removal, or deadheading, to continue blooming, but pruning off the old flowers does improve the plant's appearance. Deadheading can also prevent hollyhocks from unwanted self-sowing so they don't spread to nearby garden beds.
Pinch off any blossoms from the main stem that have begun to fade to improve the appearance of the plant. Leave the stalk in place so the remaining buds can open and flower fully. Check the hollyhocks every one to two days once the flower stalks are blooming and remove dead flowers.
Cut off the entire flower stalk at the base after 70 percent or more of the flowers have finished blooming. Use sharp shears to remove the flower stalk.
Dispose of the deadheaded stalks immediately. Stalks left in the garden bed may harbor disease organisms that can spread to the plant.
Cut down the entire plant in fall after it dies back. Remove all parts of the plant from the area.