In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl with an electric hand mixer), combine cream cheese and butter. Beat together until smooth.
Add in ½ cup powdered sweetener, mixing to combine. Add in ½ teaspoon of peppermint extract and mix to incorporate. Add 2 more cups of powdered sweetener, ½ cup at a time, mixing until dough is smooth and stiff.
Taste a pinch of the dough at this point to see if you think it needs ½ teaspoon more of peppermint extract. If so, mix/knead additional extract into the dough.
Place bowl in the refrigerator and let the dough chill for at least an hour.
Once dough has chilled, remove from refrigerator and divide the dough in half. Place the halves on a parchment-lined work surface. Add a little bit of red food coloring to one half of the dough, then knead the dough to incorporate the food coloring throughout the dough, to achieve a pink color (or the desired hue). If needed, add more food coloring until desired color is reached.
Repeat with the other half of the dough, using the green food coloring to achieve a pastel green color.
Add the remaining ¼ cup of powdered sweetener to a small dish.
Scoop the dough out by rounded tablespoon, rolling into balls (it can be helpful to add a little powdered sweetener to your hands to prevent sticking). Roll each ball into the powdered sweetener.
Place dough balls on a parchment lined baking sheet. Gently press the tines of a fork down once on each ball, flattening the balls and creating straight lines across the top.
Transfer the baking sheet to the fridge and let the mints chill for at least a couple of hours before placing them in a storage container. Keep chilled until serving, and store leftovers in an airtight container in the refrigerator.