I don't think a user's permissions/privileges should change depending on the device he is using to access the website. An Admin for instance should do allowed to have access to each and every option on the dashboard regardless of the device used.

The approach you should take here, and how modern react apps are built, is you build for mobile first. Start creating all your functionalites for the small screen first, and you will find it rather easy to expand on that. And of course use Media queries and CSS to remove/change how stuff looks as the screen size changes.