Fill a large pot with 4 quarts water, place over high heat, and bring to a boil.
Separate the Swiss chard leaves from the stalks and wash separately in cold water. Wash the mustard greens. Cut the Savoy cabbage in quarters.
Add 1 tablespoon salt to the boiling water and put in the Swiss chard stalks. Cook for 1 minute, then add the leaves. Cook until the Swiss chard is tender, 4–5 minutes. Drain in a colander and squeeze out as much water as possible by pressing on the leaves with a spoon.
Refill the pot with water, bring to a boil, add salt, and cook the mustard greens until tender, 5–6 minutes. Drain well and repeat the process to cook the cabbage. Coarsely chop all of the vegetables together.
Combine garlic and olive oil in a 12-inch skillet and place over medium heat. Let the garlic sizzle for a few seconds but do not brown. Add the vegetables, season with salt and pepper, and sauté, stirring often, for about 15 minutes. Serve at once as a side dish or over toasted bread as an appetizer.