Playing Devil's Advocate for a minute there may well be more to the story than you are aware of. It is not uncommon for management to keep ongoing performance/disciplinary issues as a private matter between the company and the employee. Alternatively are you sure you're fully aware of the severity and impact of his mistake? Many organisations will have policies and contracts with provision to skip things like warnings if the offence is serious enough.
Also it's not unheard of (although it is pretty sh*tty) for there to be a situation where a manager has been told to make headcount reductions and in those cases mistakes provide an easy get-out-of-jail-free card to do so. That's complete speculation however.
That said there is no reason not to at least have a conversation with your boss about it (once he has cooled off obviously), and when you do so I'd suggest keeping the focus on impact to the company/project. If the terminated employee really is as valuable as you say in your comment then you should be able to put together a solid business case for re-employing him. If you can't then you are probably on to a loser I'm afraid :(
When you talk to your boss I'd do so in private (that way if there are other disciplinary issues or wider business reasons he might feel more comfortable to talk to you then he would in front of others) and you might want to try an approach like this:
Hi [boss], I know you had to let [Mr X] go, I know [mistake] was really bad and I appreciate that I might not know the full story but he's a good worker and losing him may/will impact on our deadlines for the [Widget] project and depending on how long it takes us to recruit and train a replacement I'm worried about it affecting [Widget2] project as well. Is there any way we could bring him back?
That way you are keeping it rational, unemotional and focused on the business priorities - which should be exactly what you boss is focusing on as well.
But first off before you do anything to try and change your boss's mind you need to speak to the ex-employee and sound out whether he would want to come back. It's quite feasible that he wouldn't and there is no sense in sticking your neck out if he doesn't want to return!