Put grapes into a blender or food processor and pulse just briefly, about 3-5 times. Although you can vary the exact consistency, you want to be careful not to fully puree or completely liquify the grapes.
Spoon the grape chunks into six 3-ounce popsicle molds, dividing evenly. Gently tap the molds on the countertop or use the spoon to press the grapes down.
Pour any grape juice that remains in the blender/processor evenly over all the pops. This little bit of liquid will help to "glue" the bits of frozen grapes together as the popsicles freeze.