I know what this means: "To pay one debt by incurring another" or other variants of it, but where did the saying come from. I'm not aware of any biblical instance of this.
Deep down I want this to somehow involve Peter, Paul and Mary... :)
The origin comes from the Peter tax and the Paul tax:
The Peter tax referred to the tax that people had to pay to fund the building of St. Peter's Church, while the Paul tax referred to the tax that the people had to pay to fund the building of St. Paul's Cathedral.
When the idiom says "rob", it takes that if you don't pay a tax, you are robbing a person (pope, in this case) of what that person rightfully deserves.
Thus, the saying means, not paying the Peter tax in order to pay the Paul tax.
We don't normally like to give links to other resources as StackExchange answers but I think you'll struggle to find a more comprehensive answer than this one:
In essence the expression is very old, possibly dating to around 1380, but there is ongoing discussion around why the names Peter and Paul were chosen.