Stir together blood orange juice and pomegranate juice in a large serving bowl. Chill at least 2 hours or up to 24 hours.
Stir in ginger ale and orange slices.
Serve immediately.
*Sweet red grapefruit juice may be substituted.
Pomegranate-Orange Punch: Prepare recipe as directed, omitting ginger ale. Stir in 3/4 cup chilled vodka, 1 cup chilled orange liqueur, and orange slices before serving. Makes 6 3/4 cups.