Copying MySQL table to another table with no missing new changes
The way you provide is a very simple and basic level's solution to create a backup copy of the table. Once copy done and someone made a change into the main table backup won't be updated with original tables so you have to do it again.

As far I understand you want to keep backup of your whole database which should be up to date with all changes being done till now.

To make this you can create a master-slave replica of the database, which will work as a master-slave database. Changes being done in the master will automatically reflect in the slave database.

Thank you.