Place asparagus and peas into a small skillet or saucepan and cover with water. Bring to a gentle boil and cook until asparagus are bright green, about 1 minute. Immediately remove from heat, drain, and place asparagus and peas into an ice water bath to stop the cooking. Let cool and drain.
In a large bowl, toss cooled asparagus and peas, snap peas, arugula, radishes, mint and pistachios.
In a small bowl, whisk together lemon juice, olive oil, salt and pepper. Pour over salad and toss to coat. Refrigerate until ready to serve.