Rinse the quinoa in a fine-mesh sieve. Put it in a medium saucepan with the water and bring it to a boil; reduce the heat and simmer, covered, for 12 minutes. Remove from the heat and let stand for 10 minutes. Remove the cover and fluff with a fork. Cover and refrigerate until chilled.

Stir together the quinoa, grapes, cheese, lemon juice, and mint in a large bowl. Top with green onions, if desired.