Slice 3-4 thin rounds of cucumber and soak in ice water for 10 minutes to firm up for garnish.

Peel and chop 1 medium cucumber into small pieces to yield 1 cup, then place in the blender.

Blend the chopped cucumber with the sweetener and mint leaves, along with 1 cup of cold water, until smooth.

Strain the mixture through a fine-mesh strainer into a bowl to separate the liquid from the pulp.

In a large pitcher, combine the strained liquid with lime juice and black salt, and add 2 cups of water.

Serve by placing cucumber slices in glasses, adding ice cubes, and pouring the cucumber mixture on top.