Set your oven at the lowest temperature possible (170°F). Line a baking sheet with parchment paper. Carefully pour the blackberry puree onto the baking sheet, spreading the puree in a thin even, layer.
Put the baking tray in the oven for 8 hours on the lowest setting. The blackberries are ready when they resemble a deep purple/brown color. Leave the dehydrated fruit out overnight for an additional drying process to allow any remaining moisture to escape.
Pull as much of the parchment paper off as possible, then start breaking the puree apart and carefully remove the parchment paper from the back. Ensure there is no parchment paper left of the hardened blackberry paste.
Put the puree pieces back into a dry food processor and blend on high speed until all of the pieces resemble a fine powder. You can use a coffee grinder in a pinch as well.
You can store the blackberry powder in glass jars with a lid. Store the powder in a dark, dry cool place in your home, keeping it accessible for later use.