Definition from Wiktionary, the free dictionary
- (intransitive) to become twisted, or turned to one side
- (intransitive) to depart from the correct course
- Of a situation, to fall apart or unravel; to fall into disorder; to hit the fan.
If something is going awry it means that the situation is falling apart in a negative sense, unraveling, gotten chaotic and disorderly, and certainly not the anticipated outcome.