The immutable truth and benefice of God was that God's will was for the American people to overspread North America. Benefice is a medieval term indicating a gift of endowment, normally a fief or title of nobility, normally awarded by a churchman. By using the term, O'Sullivan implies that God has given the continent to the Anglo-Saxon American race as an inheritance and gift.
To O'Sullivan, God had given the whole of North America to the American people as something of a "promised land" in return for which they were responsible for spreading Republican style democracy. O'Sullivan saw the destiny of the United States as something of a moral, or "higher law," so much so that it transcended International Law. Even so, O'Sullivan did not support military intervention. He believed since this was the manifest destiny of the people of the United States, it would happen inevitably with the immigration of Anglo-Saxon Americans to other areas--the culture would follow the people. Interestingly, he opposed the Mexican War, although he later stated that the result was beneficial to both the U.S. and Mexico.
I assume you are referring to O'Sullivan's article "The Great Nation of Futurity." If so, O'Sullivan argues that the "immutable truth and beneficence of God" is that all people should be free and should live under a good government and in a good society like that of the United States. This is why, he says, the US is destined to expand its territory and create a country that will be a beacon to the world.
As O'Sullivan says, America is based on the ideas of
...freedom of conscience, freedom of person, freedom of trade and business pursuits, universality of freedom and equality.
He argues that the work of the United States is to spread these ideas as far as possible. By spreading these ideas and making more people live according to them, the US will be fulfilling its mission. When it brings those things to the people of the world, it will be bringing them the "immutable truth and beneficence of God."