Measure out and combine the frozen blue raspberries, sugar, and water in a blender.
Pulse the blender a few times to start breaking down the berries and dissolve the sugar slightly.
Add the ice cubes to the blender, then secure the lid tightly.
Blend on high speed for about 30-60 seconds until the mixture is smooth and slushy, with a vibrant purple-blue color.
Pause briefly to check the consistency; if it's too thick, add a splash more water and blend again briefly.
Pour the slushie into chilled glasses, watching the colorful ice crystals swirl together.
Serve immediately with a straw or a spoon for scooping up the icy, flavorful treat.