You can create a scene called "break_effect.tscn" with the following structure:
Use your broken meteor images as the sprites.
Then you can create an animation in which you move the sprites farther apart over time, and even make them increasingly transparent by changing their modulates. You can also rotate them and build this into the animation. Just key frame all these changes into the animation as you make them.
Add a script to the main node and attach the animation finished signal from the animation player. Set this signal up so that when the animation ends, queue_free() is called. This will automatically delete the effect node.
To create this effect in your game, just instance it, position it, and add it to your scene using code. Position it at the meteor that is being destroyed.