Can I redesign a website on a back-up and than transfer it onto a main website?

I have a website that I want to redesign, and I’m not sure how to do it without deconstructing an existing one for back-up purposes.

Can I copy the website, redesign, and then transfer the changed website across by copying it to a clipboard, or do I need to transfer the domain to the redisgned one instead?

@Laleesh - The latter. You can find out how to transfer hosting in the University.