After making your way through the Canyon of Titan, you'll arrive at the Titan Temple. You will be given information either by the Diamondback Militia or the Mad Monks on a place called Silo 7, which is north of the Temple and Damonta.
When you go to Silo 7, there are a couple turrets in your way to the Silo but not much else. When you reach the nuke, you can attempt to disarm it by climbing the ladder next to it and using either Mechanical Repair or Demolitionist.
I could not get Mechanical Repair to work no matter how many points I put into it, so I'd recommend a Demolitionist skill of at least 5 to have a decent shot. If you fail, the nuke explodes and kills everyone, but you can always reload and try again.