Preheat the oven to 200 degrees F (95 degrees C).

Cook and stir ground beef and onion in a large skillet over medium heat until beef is brown and crumbly, about 10 minutes; drain excess grease.

Stir in beans, diced tomatoes, diced tomatoes with green chiles, and chili seasoning; bring to a boil. Reduce heat to low; simmer until thick, about 10 minutes. Continue simmering while making fry bread.

Combine self-rising flour and buttermilk in a bowl (dough will be very sticky). Scoop about 1/4 cup dough; gently pat into a 5-inch circle on a well-floured work surface. Repeat with remaining dough.

Heat vegetable oil in a heavy skillet to 400 degrees F (205 degrees C).

Fry 1 dough circle until golden brown, about 3 minutes per side. Fry bread will expand in size as it cooks. Drain on paper towels; place on a baking sheet. Transfer to the oven to keep warm while frying remaining dough pieces.

Top fried bread with ground beef mixture; serve.