Heat oil in a medium saucepan over medium heat until it reaches 375 degrees F on a deep-fry thermometer (oil temp will drop slightly with addition of green beans -- maintain at 350 degrees F). Reduce heat to low if it gets too hot.
Meanwhile, combine mayonnaise and chipotle in a small bowl; set aside. Mix 1/2 cup flour; the cornmeal salt and pepper in a medium bowl. Put remaining 1/2 cup flour in a second bowl and buttermilk in a third bowl.
Working with about 10 beans at a time, dust beans with flour, dip in buttermilk, then dredge in cornmeal mixture, breaking clumps apart as needed.
Carefully drop beans into hot oil, turning to keep them from sticking. Fry beans until golden brown, about 3 minutes, increasing or reducng heat as needed to keep oil at 350 degrees F. Using a slotted spoon, transfer beans to a tray lined with paper towels. Serve with spicy may on the side.