How to Cut images/writings and moving it?

27507288zsob,

As I (mis)understand it, you can, starting with the original linked image (avoid embedding):

1) Copy the image as many times as you have parts to move round and lock the original;

2) For each part, create a suitable closed path round the part without including anything else, then ShiftClick the topmost linked image copy from 1), then hold Ctrl/Cmd and press 7 to create a Clipping Mask, then ClickDrag into the desired position.

This ought to give the desired appearance, although you may have to work (maybe even hard) with differences in the background colour (transitions).

You can use the legacy Save for Web or Export the final appearance to create an edited image.

If you select it and cut it, you can paste it and move it wherever you want.

Open the document select the text. Copy and paste.

We are talking about AI files, right?