Place the mushrooms in a 5- or 6-quart slow cooker. Top with the stew meat and carrots.
In a bowl, mix together the tomato sauce, maple syrup, vinegar, and salt and pour evenly over the meat and vegetables.
Cover and cook on low until the meat and carrots are tender, 6-7 hours.
When done, maintain the slow cooker on low heat. In a bowl, whisk together the cornstarch and water until well blended. Gently stir the cornstarch mixture and the peas into the slow cooker and cover until the liquid thickens and the peas heat through, about 5 minutes. Serve.