Mining on Linux with an USB hard-deive I want to mine with my AMD gpu. However I don't want to install the amd sdk on my daily driver operating system because that too much dependencies and external debs for me. I have the idea to install Ubuntu 18.04LTS on a USB (not an installation usb, a real installed operating system). Would it make sense or is it not very efficent ?
That would probably work fine.  Mining doesn't generally require fast disk access, especially if you are mining in a pool.

Of course, you'll have to reboot into your Ubuntu installation each time you want to start mining, and you won't be able to use your "daily" operating system at the same time as mining.