To juice the pomegranate, cut it in half (as you would a grapefruit) and juice using a citrus reamer or a juicer. Pour mixture through a cheesecloth-lined strainer or sieve. One large pomegranate will produce about 1/2 cup of juice.
Combine sugar, lime juice, and mint leaves (if using) in a glass. Mash leaves with the back of a spoon. Mix in rum and fresh pomegranate juice.
Fill two cocktail glasses with ice. Divide mixed mojitos between the two glasses.
Top with a splash of soda water. Garnish with an additional mint leaf and slice of lime.