If you need to know in Illustrator how to cut a shape, there are several ways to go about it including using the Knife Tool, Eraser Tool, Scissors Tool and Crop Tool.
How to Cut Out an Image in Illustrator in 8 Steps
Draw and edit shapes in Illustrator on the iPad
How to Cut Out Shapes in Illustrator
Illustrator: How to cut out a circle from the middle of a shape with effects? - Graphic Design Stack Exchange
4 Easy Ways to Cut a Circle in Half in Adobe Illustrator
How to Cut a Shape in Half in Adobe Illustrator - imagy
2 Ways to Use Slice Tool in Adobe Illustrator (Examples)
4 Easy Ways to Cut Out Images in Adobe Illustrator
How to Cut a Shape in Adobe Illustrator - Bittbox
Easily cut, divide, and trim artwork