Is there a database or study where Quran ayahs are cross referenced? (I would be very surprised if not, as that be an infinitely useful way to study and understand Quran.)
I think there is no such a thing like softwares or databases and interested people can go through Tafseer books.
Tafseer Al-Mizan authored by Allamah Muhammad Hussein Tabatabai is one of most notable of them.
But some books, named Kashf-u-al-ayat (
کشف الآیات) (discovering the verses), can be used for this purpose. In fact, they have indices that you can find verses from roots of words.