I'm the guarantee host for a tourist visa for my former girlfriend. Now she got the visa in her passport, but we just split. Is there a way to cancel the visa? She alread got the passport with the visa. Can the visa be cancelled by me without the need for her to bring the passport to the embassy? Is there a database for all visa were the visa can be canceled and therefore the entry in schengen can be denied?
A Schengen visa can be revoked. From the Schengen Visa Code:
A visa shall be revoked where it becomes evident that the conditions for issuing it are no longer met. A visa shall in principle be revoked by the competent authorities of the Member State which issued it.
So, as mentioned in the comments by Lily, you can inform the consulate that issued the visa that your girlfriend is now your ex-girlfriend. They may decide to revoke the visa, but they may decide not to.
The code provides for no requirement that the visa holder be notified when a visa is revoked, beyond the visa being stamped "REVOKED"; this presumably would happen at the border when she is denied entry. There may be some policies about notifying visa holders where possible, but this is not required by the code, so it perhaps varies from country to country.
I do not think that airlines have the ability to query the Schengen databases to confirm the validity of a traveler's visa, but I could be wrong. In any event, if she "already went to the airport," as you mention in a comment, for her trip to Italy, it's almost certainly too late. It's highly unlikely that there is enough time for you to inform the consulate and the consulate to make a decision to revoke the visa before she gets to the airport.
If you are worried that she might get you in trouble by doing something you have guaranteed that she wouldn't do, then maybe you should ask a separate question about that.
A Schengen visa can certainly be cancelled (technically revoked and/or annulled depending on the circumstances) and such a cancellation would indeed be recorded in a database… but you cannot cancel it. After all, you did not issue it in the first place. Also, why do you care?