Cook beef in 12-inch skillet over medium-high heat about 10 minutes, stirring occasionally, until brown; drain.
Mix tomato puree and mushroom soup in medium bowl. Stir in onion soup and water.
Spray 5- to 6-quart slow cooker with cooking spray. Reserve 1 cup of the potatoes. Gently mix beef, remaining potatoes, carrots, salt and soup mixture in cooker. Sprinkle with reserved 1 cup potatoes the add cheese.
Cover and cook on low heat setting 6 to 8 hours, depending on size and shape of your crockpot. Cook until vegetables are tender. Hash will hold on low heat setting up to 2 hours.