Add potatoes and chopped onion to the bottom of a slow cooker. Drizzle with olive oil and season with salt, pepper, and Cajun seasoning. Toss to coat evenly.
Layer the sliced smoked sausage and green beans on top. Sprinkle with onion soup mix and garlic powder. Place pieces of butter evenly over the top.
Cover and cook on low until the potatoes are tender and everything is well flavored, 6–7 hours, stirring a few times throughout the process and just before serving.