Bring a large pot of water to a boil and season water with salt. Add pasta and cook according to instructions on the package.
In the meantime, in the bowl of a food processor, add pistachios, garlic, mint leaves, and salt. Put on the cover and turn on. Drizzle olive oil through the feed tube until mixture is combined and resembles pesto. Remove mixture and place into a large glass bowl.
Once pasta is done cooking, drain and add the hot pasta to the glass bowl, on top of the pistachio pesto mixture. Toss pasta together with the pesto until pasta is coated with the pesto. Add the cherry tomatoes and toss to mix. Season with additional salt and pepper, to taste.