Place the fresh berries, sugar or honey, and water into the blender. Blend on high until the berries are completely broken down and the mixture is smooth with no chunks.
Pour in the rum and add the ice cubes to the blender. Secure the lid tightly.
Blend on high speed until the mixture transforms into a thick, slushy texture, with ice finely crushed and evenly distributed.
Stop the blender and check the consistency. If you prefer it thicker, add a few more ice cubes and blend briefly.
Taste the slushie and adjust sweetness if needed by adding a little more sugar or honey, then pulse briefly to incorporate.
Pour the frozen rum berry mixture into tall glasses. Garnish with extra fresh berries or a sprig of mint if desired.
