Grind the cranberries or chop them medium-coarse in a food processor, using the steel blade.
Combine the cranberries, water, and sugar in a saucepan. Bring to a boil, then reduce the heat, cover, and simmer, stirring occasionally, until the fruit is entirely translucent, 10 to 15 minutes.
Force the pulp through the finest disc of a food mill, then pre