Cook the chorizo over medium-high heat in a large saucepan until browned, about 3 minutes. Spoon off and discard any fat.
Add the leeks and garlic and cook, stirring until slightly soft, about 2 minutes.
Add the tomatoes and their liquid, 2 cups water, ½ teaspoon salt, and ¼ teaspoon pepper and bring to a boil.
Stir in the grits. Reduce heat to medium-low and cook, stirring often, until the grits are tender and slightly thickened, about 10 minutes.
Add the corn and spinach and cook, stirring, just until the spinach wilts. Divide among individual bowls.