Cut the cucumber into 4 lengthwise pieces and then cut in half in the middle to create 8 pieces of cucumber.
Place cucumber into a food processor or blender. Blend until the mixture is smooth and like a thick juice. This will likely take 2-3 minutes of blending.
Place a fine strainer over a medium bowl. Pour mixture into a fine strainer and use the back of a medium spoon to push the cucumber into the sides to get all of the juice from the cucumber into the bowl. Discard the solids when strained completely.
Fill 4 12 oz glasses with ice. In a shaker, add margarita mix, cucumber juice, and tequila. Shake a few times to combine and pour into the glasses.
Garnish with lime and cucumber. Enjoy!