Add the water, the watermelon pieces, the lime juice and the peppermint leaves to your blender and mix on high speed until smooth. You might experience that not all of the watermelon pieces fit in at once; if that happens, start off by blending half of the watermelon pieces and adding the rest bit by bit.
If you're using bananas, peel them and add them to the blender too.
If you're making a cocktail, add in white rum to your taste.