This is really easy. Just open a SSH command prompt to your server or set up a cronjob.

Then use this command:

touch /var/cache/mod_pagespeed/cache.flush

Wait a few seconds and then refresh your page in a browser to see the new content.

I would recommend to do this only if somehow the old content got stuck and doesn’t update anymore…

Normally Mod Pagespeed from google should detect changes to your files automatically and serve the most recent one.