1. The idea is not to shatter it. The idea is to ablate material off of the surface as a kind of "rocket motor" to change its course so that it misses the earth.

2. Even if it shatters, much of the mass should miss earth. See #1.

3. Even if all of the mass hits earth (or at least earth's atmosphere), 36 separate pieces is still much better. A meteor's ability to do damage is proportional to its kinetic energy, which is proportional to its mass - except that the first part of the damage is taken by the atmosphere, not by the ground. Spreading that around 36 separate places in the atmosphere leaves less of it to hit the ground, and that will be spread out, too, not concentrated in one place.

36 city killers is still far better than one planet killer.