Combine sliced carrots and diced carrots in a large pot. Pour enough water into pot to just cover the carrots; bring to a boil and cook until tender, about 8 minutes. Drain water completely from carrots. Transfer drained carrots to a large bowl.
Gently toss Spanish onion and green bell pepper together with carrots.
Whisk tomato soup, white vinegar, vegetable oil, sugar, mustard, and salt together in a bowl until the oil is completely integrated.
Drizzle tomato soup mixture over carrot mixture; gently toss to coat entirely.