You don't need to call the State Department, nor the Mexican Consulate.
First, you may want to review Section I.8 of the Permit to Report Booklet. I've copied it below for your reference:
"Complete the Standard Form-86 to the best of your ability and return in the manila envelope addressed to the “Commandant of Midshipmen.” This form is required to process you for a SECRET clearance. You will need to provide specific information on the SF-86 worksheet that will be returned to you following Plebe Summer to assist you in completing an online, computerized SF-86. Make sure you answer all the questions accurately so that you do not delay your clearance...
The possession and use of a foreign passport in preference to a U.S. passport raises doubts as to whether the individual’s allegiance to the United States is paramount. Clearance will be denied or revoked unless the foreign passport is surrendered. Anyone who possesses a foreign passport must return the passport to the appropriate country’s embassy or consulate, requesting a return endorsement. In lieu of returning the passport, it may be brought to the USNA Personnel Security office for documenting and witnessing its destruction. If you choose to return the passport the endorsement will be a prerequisite to any security clearance determination and must be provided to the USNA Personnel Security office when the online SF-86 is submitted."
The entire procedure will be facilitated by the USNA Security Office. In that same section of the Permit to Report booklet, it gives you a contact in the Security Office if you have questions. I just didn't want to publish his name in an open forum, but you can look it up.
If you had a passport, you would have to surrender it and witness its destruction. You are also asked to sign something indicating that you are willing to renounce your foreign citizenship. Whether you are actually required to do so is a decision that is made by the Security Office during their investigation.
The most important thing is to declare your dual citizenship on the SF-86. Navy will take it from there.