vector - Making transparent but still hiding any objects below in Illustrator

Hello I am new to Illustrator (I was working with photoshop a few years). How can I fix this problem?

Answer

Either:

1. 
   

   Manually cut the paths, probably using the Scissors Tool (C).

   
   


2. 
   
   

   Use pathfinder operations (Window → Pathfinder).

   
   

or

3. Define a transparency knockout group.