In a food processor, whirl garlic to mince. Add 4 cups grapes, 1/3 cup almonds, 4 tbsp. vinegar, 1 tbsp. oil, 1/4 cup water, 1 tsp. salt, and white parts of green onions; whirl until almost smooth. Transfer to a bowl. Put chopped cucumbers, 1/3 cup almonds, and 1/4 cup water in food processor; whirl until almost smooth and add to bowl.
Stir soup to blend, then chill, covered, at least 2 hours.
Cut remaining 1/2 cup grapes in half. Season soup to taste with more vinegar and salt if you like. Divide among four bowls and top with a little sliced cucumber, green parts of green onions, and some of remaining grapes and almonds. Drizzle with oil and serve remaining toppings on the side.
Make ahead: Through step 2, up to 1 day, chilled.