How to track changes between nightly MySQL database dumps
What you're referring to is called a delta, incremental, or differential backup, which is certainly natively supported by MySQL. You might want to consider backing up the deltas to an intermediary database that you can run your reports off of.  That data can then be added to the up-to-date DB.

I would suggest using an administration tool like Navicat for MySQL for setting up the backups.  It makes it easy to schedule and configure the backup rules.  You can compare and sync data between databases/schemas with detailed analytical wizard process.



As a bonus, it can produce really eye-catching reports.

Hope that helps!