When something self-destructs, it destroys itself. In the military, weapons such as land mines are intended to self-destruct.
There are bombs and rocket boosters that are programmed to self-destruct as they perform their jobs, and you can also use this verb in a figurative way when someone acts in a way that harms themselves. If your friend is missing school, failing tests, and alienating his friends, you might worry that you're watching him self-destruct. The first known use of self-destruct was in the 1960s TV show "Mission: Impossible."