If you were to do that, you'd be forcing your customers to wait a lengthy period of time for your server to do all its database queries across a (slower-than-if-it-were-on-same-server) internet connection. While it "can" be done, it's *strongly not recommended*, and has several caveats.
Doing it requires editing your configure.php files to point the DB_xxxx settings to the other server, and you also need to open the other server's firewall to allow direct remote access to the server's database from internet connections. All your database data will be transmitted in clear text, with no encryption protection. All your admin settings will be shared exactly between both sites, so you will have limited branding differentiation available. There will be various other limitations too, related to order processing.