If using fresh blackberries, wash them thoroughly under running water. Then inspect them carefully and discard any that are bruised or damaged. Gently select them one by one, and remove the stem from the top of any blackberries that have one. Let them rest in a colander after washing to drain and dry.
Wash the soursop well and dry it with a kitchen towel. Then place it on a cutting board and cut it in half. You can use a knife, but when they are ripe, simply apply a little pressure with your hands to separate them into two pieces. Place the soursop pieces on the board or another work surface, and with a spoon, scrape all the pulp away from the rind. Place the pulp in a bowl.
With your hands, carefully examine the soursop pulp and remove all the seeds. The seeds are embedded in the pulp, so you'll need to apply a little pressure to remove them. Place the pulp in a separate bowl and carefully remove all the seeds, as they can make the smoothie bitter when blended.
In a blender, combine the soursop pulp, one-third cup of sugar, two cups of water, vanilla (optional), and ice to taste. Blend for about three minutes until smooth. Pour the juice into glasses.
Rinse the blender jar briefly and add the blackberries, one cup of water, the remaining sugar, and ice to taste. Blend for approximately five minutes. Strain the mixture immediately and pour it over the soursop juice. The two mixtures will blend, but not completely.
You can garnish the smoothie glass with fresh blackberries. Serve immediately.