In a saucepan, combine the raspberries, 1-3/4 cups water and sugar. Bring to a boil. Reduce heat; simmer, uncovered, for 30 minutes.
Mash raspberry mixture and strain through a fine sieve into a 2-cup measuring cup; discard seeds. Add water if needed to make 2 cups puree. Return to the saucepan.
Combine cornstarch and remaining water until smooth; gradually stir into raspberry mixture. Bring to a boil over medium heat, stirring constantly. Cook and stir 1 minute longer. Remove from the heat; cool. Store in the refrigerator.