Warm the olive oil oil in a large saucepan over medium-low heat. Stir in the garlic and lower the heat to low. Fry for 2 minutes, then add the canned tomatoes and bring into a boil. Stir in the olives and capers. Lower the heat and simmer, with the lid on, for 40 minutes, stirring occasionally.
Preheat the oven to 400°F/200°C. Line a baking tray with baking paper.
Rinse the sweet potatoes carefully and dry. Slice them not too thin and not too thick, about 1/2 inch. Place them on a baking tray in one layer and brush with oil. Sprinkle salt, smoked paprika and oregano and bake for 15 minutes or until the potatoes are golden brown.
To serve: put 5-10 sweet potatoes in deep plates, ladle puttanesca sauce over, drizzle a little bit of olive oil and sprinkle crushed chili.