Heat coconut milk with mint leaves and simmer in a saucepan for 4-5 minutes. Remove from heat. Strain the leaves out and set the coconut milk aside to cool.
Combine lime juice and blueberries over low-medium heat in a saucepan for 4-5 minutes to create a sugar-free compote. Allow the compote to completely cool.
Once the coconut milk is room temp, fill up six popsicle molds about 3/4 of the way. If using large molds, add a small amount of water to each to add volume if needed. Place in the freezer for 30-40 minutes until slightly set.
Remove from freezer to swirl in the fruit compote. Add popsicle sticks to the center of the molds and place in the freezer for a minimum of two hours, or until popsicles have completely frozen.