you can download all whole site or just downloading the theme file, plugins and database, then install wordpress locally (do you know how to build local server using xampp, mamp or kind of that?) after that you can preview your site offline (of course)
but all changes will be stay offline, as far as i know, there is no way to make your changes or new content will be sync to live server.
i suggest you tried new desktop wordpress app http://desktop.wordpress.com it can installed and you can post it offline, then when you connect to internet, you can publish it and it will post to your live server site.
Moderator
t-p
(@t-p)
As Yoga and Tara pointed out, this is definitely possible and also pretty common.
You can also use a plugin called Migrate DB to download the database of your WordPress site on your server and then upload the database to your local installation. This way you will copy the exact content of your remote site to your local one.
And as Yoga wrote, all changes on your local site will stay there. You need to upload changes manually, e.g. using FTP.
If you want to have a more bullet-proofed workflow, you should look at something called “deployment“.
Another way (or plugin) to do it is by using Duplicator.
https://ww.wp.xz.cn/plugins/duplicator/
- Duplicate your live site to your local
- Make changes in your local
- Duplicate back from your local to your live site
Of course this is a simplified workflow.
If you’d like to know more about Duplicator, try following this guide:
http://wplift.com/cloning-duplicating-wordpress-website
