The only way to kill the driver without destroying the tank is to pull the driver out by one of the following:
- Trying to get in, which is pretty suicidal (assuming the driver hasn't locked the tank, of course)
- Calling Lamar to set a mugger on the driver to pull him/her out. This method requires you to be at least level 50.
Luckily, a tank is not completely unstoppable. It's not like in previous GTA games where it could take an infinite amount of car explosions when driving over them. It's also vulnerable to grenades, sticky bombs, the grenade launcher, RPGs, other tanks and the rockets of buzzards and fighter jets.
I haven't met anyone who shot it with an RPG (requires level 100) yet, but I can imagine that it's even more devastating than other explosive weapons.