We had a purchasing manager at our chemical company that was the first (open) office a salesperson would hit if they walked in to try to sell something unannounced. I used to cherish the times when I’d catch him just tearing a sales guy a new booty-hole. It was amazing, especially when he’d give them enough rope to hang themselves by admitting they had no idea what we made or purchased even though they were certain they could get it better and cheaper.
You hire them in good faith believing they will be a good employee, then you give them every opportunity to be a good employee, which means letting them know when they aren’t meeting the standard. Lastly, you make sure that letting them go is the best thing for the company and other employees and make the exit as painless as possible by helping them where you can and providing feedback that will help them in the future. After that it’s just about accepting that you did the right thing even if you feel bad for it.