To do this, you can use Tableau Online Sync: Schedule Refreshes for On-Premises Data.
In a nutshell, you can install Tableau Desktop on a machine with connection to the server running MySQL and schedule the task there. Ideally, this machine won't be shut down very often, so it'll probably be some kind of server (perhaps even the same computer running MySQL).
One license of Tableau Desktop allows you to install it in 2 devices, so you could still keep it on your desktop and on this other machine that will be refreshing the extracts.
Hope this helps!