If my staff issue a flight ticket by mistake, can I cancel it straight away without losing the whole fare?

Often yes, if you act quickly. Many airlines allow a ticket to be voided within a short window after it is issued, usually the same working day, and a void is not the same as a refund. A voided ticket is treated almost as if it was never issued, so the money comes back in full or very close to it, and it comes back far faster than a normal refund would.

Whether the option is there depends on the airline and on the supplier the fare came through. Some low cost airlines do not offer a void at all, and some suppliers do not pass the option on to you even where the airline allows it. Once the window has closed, the ticket stops being a mistake you can undo and becomes an ordinary cancellation, which means the fare rules decide what your customer gets back and the airline may keep part of it.

Because the window is short, the practical answer is to treat a wrong ticket as urgent rather than raising it as a normal support request the next morning. Have your team check the passenger name, the date and the route on the booking screen before they confirm, since almost every void request comes from something that could have been caught in that last look.

If it has already happened, open the booking on your portal and see whether a cancel or void option is offered, and if it is not, contact your account team the same day rather than waiting.