To give someone the sack, also: to sack someone; to get the sack
If she comes late again we’ll have to give her the sack.
They sacked him for hitting a colleague.
John got the sack from his last job.
To give someone the sack or to sack someone means to fire or dismiss them.
(Note: This term is used when someone loses their job because of their own behaviour, not due to the company going through a bad patch or the general economic climate. If a person loses a their job through no fault of their own they are laid off or made redundant.)
The expression comes from a time when a worker brought his own tools to work in a sack. When he lost his job he was given this sack back.
German: jemanden feuern
By the way:
Not to be confused with the expression to get someone in the sack ( = jemanden ins Bett kriegen) 😉