Using a large chef's knife, cut the watermelon in half lengthwise through the stem. Trim a small portion from the underside of each half so it can sit on the work surface without wobbling. Transfer to a rimmed baking sheet. Scoop out most of the flesh with a large spoon into a medium bowl, leaving about 1/8 inch of flesh above the white part of the rind (this will help the gelatin to adhere).

Transfer the watermelon flesh and any juice from the bowl and rind to a blender and puree until very smooth, about 2 minutes. Strain through a fine-mesh sieve lined with cheesecloth (or a coffee filter). Discard the solids and reserve the juice; you should have about 5 cups total.

Measure 3 cups of the juice into a medium saucepan (save any remaining juice for another use). Bring to a simmer over medium-high heat.

Meanwhile, whisk the watermelon-flavored and unflavored gelatin with the citric acid together in a large bowl, then whisk in the warm watermelon juice until all of the gelatin has dissolved, about 2 minutes. Whisk in the vodka until combined. Pour the gelatin mixture into the hallowed-out watermelon halves. Transfer to the refrigerator and chill until completely set, about 4 hours and up to 24 hours.

Slice the watermelon in half lengthwise, then crosswise into small wedges. Serve chilled.