The pest is more likely slugs. Cut worms cut off the plant. sand ,diatomaceous earth, small gravel will deter them. There are snail/slug baits on the market that work well. Many folks over the years have used saucers of beer to trap them. Cut worms have to wrap the selves around the stem to cut them, so one old time trick is toke a stick into the ground right beside the plant. Any twig will do altho uptown folk use popsicle sticks. Cutworms are also easy to find. They will be under the soil at base of the plant the morning after cutting. Never had one cut a sunflower, but sunflowers are a slug magnet.
