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 checkmark 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.