I prepared my Linux Mint usb, and it works fine. I downloaded minecraft, ran it fine, then i used the USB again today and it did not have minecraft on it anymore. I prepared the USB with rufus, and it has 64 gigabytes of storage, although only 3 are partitioned.
In order for your actions on the live usb to have lasting effects, you'll need to set up a persistence partition when you flash the drive. Still using Rufus, when you select the ISO a "Persistent Partition Size" slider should appear, allowing you to set how much persistent storage you wish to create.