I think some people are having trouble understanding the concept that if a Pope becomes a heretic, he ceases to be Catholic, in which case he is no longer the Pope. Think of it this way. If the President of the United States renounces his citizenship, then he is no longer an American. This also means that he is no longer the President, because in order to be president, one must be an American citizen.
Uh, no. One has to be a native born citizen to be elected president.
Article II Section 1 Clause 5. No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
Once in office, there is nothing preventing him from renouncing his citizenship and still retaining office. The US has a remedy for that though:
Article II Section 1 Clause 5. In Case of the Removal of the President from Office, or of his Death, Resignation, or Inability to discharge the Powers and Duties of the said Office, the Same shall devolve on the Vice President, and the Congress may by Law provide for the Case of Removal, Death, Resignation or Inability, both of the President and Vice President, declaring what Officer shall then act as President, and such Officer shall act accordingly, until the Disability be removed, or a President shall be elected....
Section 4. The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other High crimes and Misdemeanors.
Just because he renounces his citizenship, unless he also resigns, he must be removed by impeachment. He does not automatically cease being president.
Your Vatican doesn't have the escape clause in its canon law. Once validly elected and accepted, you are stuck with your supreme pontiff with no means of removing him, except killing him.