I haven't found a way to do so in the UI.
I asked a dev but haven't heard back yet.
You can delete them directly from the database.
They are saved in ost_queue.
You can locate it by its title.
You can find its title under Tickets -> Search on the agent panel.

In this example I created a search called "Abatha". When I go to the ost_queue table I see it there.

I just delete this row and its gone. I have not seen any bad behavior since deleting this one directly from the database.