You can cut one object or group from another with the Cut Tool. There are two ways to access the Cut tool:
Keyboard: C G
Run the Cut command and follow the mode instruction in the upper left of the screen
Single click to Select an object to cut into
Single click to Select an object(s) or group(s) to be removed
Click the check mark to finish the command. The object that was removed remains in the scene. You can delete it or use Layers to hide it.
Double click to select the object to be cut into. (Single click for a Group)
Holding the CTRL key double click an overlapping object(s) to cut out.
Right click on the object that will be cut, and choose the Cut tool in the Context Menu