I decided to install a SSD on my Macbook Pro, replacing the optical drive with it, then I set up the new disk to be the boot drive and left the HDD on its place to store media and stuff.
Obviously, my library now is on the HDD, but when I try to delete a file via iTunes I get a partial elimination, or no elimination at all. The songs remain on their place on iTunes. I have no idea why. My only theory is related to the TRIM option: I have a small application that enabled it on both drives, so maybe it may be a pain for the HDD?