Make the Sauce: Combine the minced red chile pepper, green chile pepper, cooking wine, gochugaru, gochujang, soy sauce, brown sugar, garlic, and ginger in a small bowl, then mix thoroughly until the ingredients are evenly combined.
Cook the Daikon: Add the water and sliced daikon radish to a large pot and bring the mixture to a boil. Continue cooking for about 5 minutes, or until the radish becomes tender. Add the Mackerel: Place the prepared mackerel pieces into the pot with the cooked daikon, keeping the ingredients in the pot without stirring them together.
Add the Sauce: Pour the prepared chile sauce evenly over the mackerel, making sure the seasoned mixture reaches the fish and braising liquid.
Reduce the Cooking Liquid: Cook over high heat for about 10 minutes, occasionally spooning the cooking liquid over the mackerel without stirring the mixture. Continue until the liquid has reduced by approximately half.
Simmer the Mackerel: Reduce the heat and partially cover the pot. Simmer for about 15 minutes, allowing the sauce to continue reducing until it becomes noticeably thicker.
Garnish the Dish: Scatter the sliced green onions over the cooked mackerel before serving.