You shouldn't think of all firing as a "mistaken hire". Sometimes you hire someone, and they work effectively for years, and then they kind of "check out" and don't do much work any more. It can be a good decision to hire someone, and then later a good decision to fire them.

It's also not a cost-cutting measure per se. Typically when you fire someone you get to replace the headcount with another hire or internal transfer. The point of firing people is to get rid of low performers and replace them with high performers.