Add sugar, mint, and lime wedges to bottom of a large dish. Using a muddler or the back of a spoon, break up mint and lime to release mint oils and lime juice. Pour Bacardi Rum over and stir to combine.

Add watermelon to rum mixture and let soak 1 hour.

Line 2 large baking sheets with parchment paper. Remove watermelon from rum mixture and brush off any mint leaves. With a paring knife, make one small cut into rind of each watermelon wedge and gently push popsicle sticks into place. Arrange in a single layer on prepared baking sheets. Freeze until solid, at least 2 hours.

Serve watermelon popsicles garnished with lime zest and chopped mint.