You are looking at the wrong document. To find out where secession is articulated to be a natural right given by God, go to the mother of the US Constitution; The Declaration of Independence.
There was no need to articulate a right to secession in the Constitution. Coming along 11 years after the Declaration, the principles articulated in the Declaration were clearly remembered and understood in 1787.
In fact, it makes no sense that a nation which created itself under the premise that secession is a natural right of a people, could deny such a right in any other case.
Indeed, Lincoln himself twice articulated the position that people had a right to independence if they wanted it.
The Declaration of Independence had no legal standing in the Law of the United States. It is not part of any USC.
Actually the constitution is talking about rebellion, not secession, there is a difference.