If you have a copper mug, use it for a more authentic Moscow Mule drink. If you don't have one, use any sturdy glass or cup. *note: if you are going to strain out the shredded ginger and mint, use a different cup to ”muddle” ingredients so you can strain into copper mug later.
Add fresh lime juice, vodka, shredded ginger and mint sprig to bottom of cup and muddle (or mash together with a blunt utensil if you don’t have a muddler) to combine flavors.
You can strain the ingredients into your copper mug at this point if you don't like the idea of shredded ginger in your final drink). Once strained (or not) add ice to the mug and top off with diet ginger ale. Garnish with mint if using.