It seems to me that the tool you're looking for is the Pathfinder. The Pathfinder allows you to combine objects in different ways, be it merging them into one whole or, like in your case, subtracting a shape from one behind it. You'll most likely want to use the "Minus Front" option. What this will essentially do is punch a star shaped hole in the shape below it. Just make sure your paths are arranged in the correct way (so that the star is on top) in your layers panel.

#Before:

#After:

It seems to me that the tool you're looking for is the Pathfinder. The Pathfinder allows you to combine objects in different ways, be it merging them into one whole or, like in your case, subtracting a shape from one behind it. You'll most likely want to use the "Minus Front" option. What this will essentially do is punch a star shaped hole in the shape below it. Just make sure your paths are arranged in the correct way (so that the star is on top) in your layers panel.

Before:

After: