Prepare a water bath canner, along with jars and lids.
Rinse the raspberries and discard any stems, leaves, or spoiled fruit.
Add the raspberries and water to a large stainless steel pot and crush with a potato masher. Bring to a boil over medium-high heat, stirring frequently.
Reduce the heat, cover loosely, and boil gently 5 to 10 minutes, stirring and crushing occasionally, just until the berries have softened and fallen apart.
Transfer the hot fruit to a dampened jelly bag, or a colander lined with several layers of damp cheesecloth, set over a deep bowl. Let drip undisturbed at least 2 hours or overnight. Do not squeeze the bag if you want clear juice.
Optional, for clearer juice: refrigerate the strained juice overnight to let sediment settle, then carefully pour off the clear juice and discard the sediment.
Pour the juice into a clean saucepan. Add the sugar, if using, and stir to dissolve. Heat the juice to 190°F over medium-high heat and hold it there for 5 minutes, adjusting the heat as needed. Do not boil.
Ladle the hot juice into prepared jars, leaving 1/4 inch headspace. Wipe the rims, center the lids, and apply the bands fingertip tight.
Process in a boiling water bath for 15 minutes for half pints, pints, or quarts, adjusting for altitude (see notes).
Turn off the heat and let the jars rest in the canner 5 minutes. Remove the jars and cool undisturbed 12 to 24 hours, then check the seals.