In a microwave-safe mug (at least 12 ounces capacity), whisk together the flour, sugar, baking powder, and salt with a fork until no lumps remain.
Blend fresh seedless watermelon chunks in a blender until completely smooth, then measure out 3 tablespoons of the puree.
Add the watermelon puree, oil, vanilla extract, and food coloring (if using) to the dry ingredients in the mug. Stir gently with a fork just until combined, about 15-20 strokes, being careful not to overmix.
Tap the mug gently on the counter 2-3 times to release any air bubbles trapped in the batter.
Microwave on high power for 60-90 seconds, depending on your microwave wattage. The cake is done when the center is just set and springs back lightly when touched.
Let the mug cake rest for 1 minute to finish cooking with residual heat and cool slightly before eating directly from the mug or inverting onto a small plate.