Heat the oil in a large pot over medium heat. Add the garlic and cook until golden but not browned, about 1 minute.
Add the tomatoes and their juices, red pepper, oregano, 1 teaspoon salt, and sugar. Bring to a boil.
Reduce heat to medium-low and simmer (crushing the whole tomatoes with the back of a wooden spoon) until the sauce thickens slightly, about 20 minutes.
Add the mussels, cover, and cook until they open, 4 to 6 minutes. Remove and discard any that don’t open.
Meanwhile, cook the linguine according to the package directions. Add the linguine and parsley to the sauce and toss.