Heat oil in a large skillet over medium-high heat.
Add beef and sausage and cook, breaking up the beef with a wooden spoon, for 5 to 6 minutes. If necessary, transfer to a colander and drain any extra fat, then return to the skillet.
Add chili seasoning; cook over medium-high heat, stirring, until fragrant, 1 to 2 minutes.
Stir in water, tomato paste and vinegar until combined.
Transfer the meat mixture to a 5- to 6-quart slow cooker.
Stir in onion, peppers, corn, olives and garlic. Add tomatoes with their juice.
Cover and cook on High for 4 hours or Low for 7 to 8 hours.
Stir the picadillo to combine and season with salt and pepper.