It is quite easy. Just make a Live Linux USB stick (I prefer the Mint 32 bit) using the free tool
UNetbootin. The stick automatically makes itself after you choose Mint (it downloads the image, etc.), then simply boot the laptop from the USB stick and click on your drive to mount it, you can then move the data to any other drive that you attach and click on (mount).
The Mint build runs only from the USB and does not write anything to your SSD.