I don't normally cut the branches off, except this one is going in my studio so I cut it up.
Through out the summer when the flowers look dried out and before the petals fall off, I cut the dead heads off and throw them into a paper bag. I leave the bag on a shelf in the garage and in the spring when its warm enough to work outside, I loosen the soil and smash the dried flowers in my fingers and they fall into the soil and reseed themselves. The seeds are attached at the end of the dry petals. They grow fast.
Now for the snapdragons, I never pull out the plants at the end of the growing year. These are annuals but they almost always come back the following spring. Same goes for marigolds.
Can you see the difference in the color of the pictures of my morning glories? I keep the seeds and replant them every year, but this year they are alot darker blue than they have been. So i'll collect the seeds soon and I wonder what color they will be next summer, Navy blue?