What you are trying to do is entirely possible with both the Linux Mint OS and the Virtual windows machine.
really all you need to do is make an ISO of your Blu-ray disk and save them anywhere you please.
You could also copy the actual media files depending on their format. And one last possibility is to use a screen capture program to record the videos. This however is not the best option as it could result in a choppy recording depending on your computers hardware and the software configurations. Still worth mentioning.
Edit:
There are some post out there about using blu-ray on Linux. Take a look at this post. Can linux play blu-rays?