Place the cucumber in a blender and blend on high speed until the cucumber is completely liquified. Work in batches if there is too much cucumber to fit in the blender at once or if it isn’t blending.
Add the mint and blend until pureed.
Set the fine mesh sieve over a large pitcher or deep mixing bowl and slowly pour the cucumber and mint into the sieve. Add half a cup of water to the blender pitcher and swish it around to release all the cucumber pulp. Pour it into the sieve.
Use a silicone spatula or wooden spoon to gently press the cucumber juice through the strainer as it drains. If it isn’t draining, use the spatula to scrape the pulp up from the sieve to let more juice through.
Stir in the lime juice or vinegar, the Electrolyte Drops and sweetener if using. Stir well. Taste and add more sweetener if desired.
Pour over ice and top off with seltzer water.
Store cucumber juice in an airtight container in the refrigerator for 2-3 days.