Gardeners: Should I prune my sunflowers?

Usually a sunflower seed produces one tall stalk and one flower. If the flower is dead, you might want to harvest the seeds when they are good and dry and save them until next spring. Harvesting tips below.

Link doesn’t work so I am flying blind.

“Harvest sunflower seeds after the flower begins to die back, and most if not all, of the petals have fallen off. Pull out a seed and open it to see if it is full. Cut off the head, leaving a few inches of stalk. Hang the stalks to dry in a well ventilated area.

Do not stack them in a box, as mold can develop during the drying process. As soon as the flowers have dried, extract the seeds by rubbing two flower heads together. They should come off of the flowerhead fairly easily.” Source

P.S. I am assuming that they did bloom?

Another option is to leave many of the dead heads for the seed-eating birds. Think how much we spend to fill our bird feeders with sunflower seeds.

Sunflowers are annuals, they bloom, they die. No pruning needed. Harvest the seed heads if they are ready and then the plant will just naturally die.
When I have grown sunflowers I leave them for the birds as @gailcalled mentions.

The only ones you have to prune are the rogue sunflowers in the seed field. When they are developing hybrid seed for sale, one bad plant can turn a $100 a bushel crop into a $10 a bushel oil seed field.

Since it’s already flowered you can prune the dead head for looks but you will get no more blooms on that plant.

I like to prune the top of the plant just as it begins to form a bud. This causes the flower to produce 3–5 (sometimes more) smaller flowers on one stalk.

Since I grow them only for their looks I can’t comment on seed production.