Prepare a water bath canner, jars, and lids. Keep everything hot.
Peel, core, and slice the apples into a large, heavy-bottomed pot (or leave the peels on if you'll use a food mill). Rinse the blackberries and pick out any stems or soft berries.
Add the blackberries and water or juice, cover, and bring to a boil. Reduce to a simmer and cook, stirring often, until the apples are very soft and the blackberries have collapsed, about 20 to 30 minutes.
Puree to your preferred texture. Keep the seeds with an immersion blender, or run it through a food mill for a smooth, seedless sauce. Keep it a true, even puree with no chunks.
Taste and add sugar if desired, then return the sauce to a full boil.
Ladle the hot sauce into hot jars, leaving 1/2 inch headspace. Remove air bubbles, wipe rims, and apply lids and rings to fingertip tight.
Process in a boiling water bath for 15 minutes for pints and half pints, or 20 minutes for quarts, adjusting for altitude.
Let jars rest in the canner 5 minutes, then cool undisturbed for 12 to 24 hours before checking seals.