They have a bunch of explosives strapped on the rocket and can give a radio command to blow the ship up. It can even decide to explode itself if the readings go haywire.

It is called the Flight Termination System and it is very common on non-manned flights now.

If that system fails, can the rocket be shot down in time?

It could be noted that manually operated flight termination systems have been used even on manned spaceflight, each and every space shuttle flight had a termination system under human ground control.