What would happen if a death row inmate saved a guard's life?

He would get a commendation before execution

The guard might say thanks

Ever hear of it happening?

Zap

Both sides of the street would want him dead?

In the U.S. depends on where he was in the appeals process. If it were still going on, the act might be considered a reason to commute his sentence to life.
If he’d already exhausted his appeals when he saved the life, the wheels of justice would proceed, and in about 10-15 years (unless he lived in Texas) he’d probably be executed.