Place the pineapple chunks and mint leaves into the blender.
Burst the mint leaves slightly by giving them a gentle bruise, then blend on high for about 30 seconds until the mixture is smooth and frothy, with vibrant yellow-green color.
Stir in the lime juice and honey or agave syrup, tasting and adjusting sweetness if needed, to brighten the flavor.
Pour the mixture into popsicle molds, leaving about a half-inch space at the top to allow for expansion during freezing.
Insert sticks into each mold and place them carefully in the freezer.
Freeze for at least 4 hours or overnight until the pops are completely firm and vibrant in color.
When ready to serve, run warm water briefly over the molds to loosen the popsicles.
Gently remove the popsicles from the molds and enjoy immediately for a cool, refreshing treat.