I want to cut it like an uploaded image and then move it one by one. Which class or object should I use?
I'd like to be able to click on individual images.

The image class https://docs.godotengine.org/en/stable/classes/class_image.html has several methods for manipulating image data.
You could get the data from the whole image and create 9 pieces of it.

To use an image you have to create an ImageTexture from it:
https://docs.godotengine.org/en/stable/classes/class_imagetexture.html#description

For clicking, the first thing I can think of are TextureButtons. You can set ImageTexture on them.
https://docs.godotengine.org/en/stable/classes/class_texturebutton.html

Buttons have signals that you can use to call your functions when being clicked:
https://docs.godotengine.org/en/stable/classes/class_basebutton.html#signals

I hope this helps.