Combine sausages and water in a large skillet over medium-high heat; bring to a boil. Uncover and cook until water evaporates, about 5 minutes. Transfer sausages to a cutting board; cool sausages until easily handled, about 5 minutes.
Slice sausages into 1/2-inch disks.
Combine apple cider and onion in the skillet over medium heat; cook and stir for 5 minutes. Add sliced sausage and orange juice; cook, stirring occasionally, until flavors combine, about 10 minutes. Stir diced tomatoes into sauce; simmer until heated through, about 5 minutes.
Bring a large pot of water to a boil. Cook angel hair in the boiling water, stirring occasionally until tender yet firm to the bite, 4 to 5 minutes. Drain.
Divide angel pasta among 6 plates. Cover with sausage and sauce.