My Mexican passport expired in 20 14 I process it for 3 years and I only have my released military card as identification. I am a legal resident in the USA and I do not have any other Mexican document. I can process my renewal with my card as id

You only need your old passport as identification, you make the appointment and pay the renewal at the time of having the appointment.

If your passport is in good condition, it does not have any observations and you took it out in 2011, you only need to present the expired passport on the day of your appointment. Although, it is always advisable to go with the original birth certificate and other identifications for any questions. If you are going to obtain a consular license, also bring proof of address in your name.