Combine cranberries, vodka, sugar, and satsumas in a food processor; process until pureed. Refrigerate 8 hours or overnight. Strain mixture through a cheesecloth-lined sieve over a bowl, pressing to extract juice. Discard solids. Stir in Grand Marnier and lime juice. Place 1 cup satsuma mixture in a martini shaker with 1/2 cup crushed ice; shake. Strain mixture into 2 martini glasses. Repeat procedure to yield 10 cocktails.