Stir together first 4 ingredients in a medium saucepan. Cook over medium heat, stirring occasionally, 10 minutes.
Spoon about 1/3 cup sauce mixture just below center of 1 tortilla. Fold bottom third of tortilla up and over mixture, just until covered. Fold left side of tortilla over mixture; repeat with right side. Roll up, and secure with wooden picks. Repeat with remaining sauce mixture and tortillas; set chimichangas aside.
Stir together diced tomatoes and green chiles and tomato sauce in a saucepan. Bring to a boil; reduce heat, and simmer 5 minutes. Keep warm.
Pour oil to depth of 1 inch into a Dutch oven; heat to 375°. Fry chimichangas, in batches, 2 minutes on each side or until golden brown. Drain on wire racks over paper towels. Remove wooden picks.
Arrange chimichangas on platter. Spoon hot tomato mixture evenly over tops, and sprinkle evenly with shredded cheese. Garnish, if desired.