The first time was soon after his regeneration. He held up a Jammie Dodger to the Daleks, claiming it to be a TARDIS self-destruct device, which would destroy both his ship and theirs. When new New Paradigm Daleks declared it non-existent, the Doctor admitted to the biscuit's true nature, and ate it. (TV: Victory of the Daleks)
He again used a fake self-destruct sequence to convince the Van Baalen brothers to help him find and save Clara Oswald, who was trapped somewhere within the TARDIS. They had one hour to find her, "until this ship blows". This one was more convincing, even counting down menacingly on a monitor. (TV: Journey to the Centre of the TARDIS)
After admitting it to be a ruse, the Doctor elaborated on his tactics:
I just wiggled a few buttons. Yeah, the old wiggly button trick. And the face. You've got to do the face. "Save her or we all die."
The Doctor's TARDIS did have a self-destruct feature though, which the Eleventh Doctor once used to blow up the ship in a dream, to get him and his companions to wake up again in the real world. (TV: Amy's Choice)
At least one battle TARDIS did have a working self-destruct, which the Sensorites activated telepathically, on Gallifrey's orders, as the Daleks had taken control of that TARDIS, among others, to seize the Time Lords' major power source, the Eye of Harmony. (AUDIO: Sphere of Influence)