rausschmeißen
to kick out
(colloquial) To force someone to leave a place, or to dismiss someone from a job.
Nach dem Streit hat der Wirt ihn aus der Kneipe rausgeschmissen.
After the argument, the landlord kicked him out of the pub.

to throw out / kick out
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to kick out
(colloquial) To force someone to leave a place, or to dismiss someone from a job.
Nach dem Streit hat der Wirt ihn aus der Kneipe rausgeschmissen.
After the argument, the landlord kicked him out of the pub.

'Rausschmeißen' (to throw out / kick out) is a separable verb. The prefix 'raus-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er schmeißt seine alten Zeitungen raus.
He throws out his old newspapers.
The word consists of 'raus' (short form of 'heraus', meaning out) and 'schmeißen' (colloquial for 'werfen', to throw). So the literal meaning is 'hinauswerfen' (to throw out).
Kannst du bitte den Müll rausschmeißen?
Can you please throw out the trash?
This verb is very informal and is used mainly in spoken language. It should be avoided in formal situations or in written language.
Mein Chef war so wütend, er wollte mich am liebsten sofort rausschmeißen.
My boss was so angry, he wanted to kick me out on the spot.
You can recognize the meaning from the object: If the verb refers to a person, it means 'hinauswerfen' (to kick out) or 'entlassen' (to dismiss/fire). If it refers to a thing, it means 'wegwerfen' (to throw away).
Der Clubbesitzer hat den betrunkenen Gast rausgeschmissen.
The club owner kicked out the drunk guest.
When saying where someone is being kicked out from, you use the preposition 'aus' with the dative.
Sie wurde aus der Bibliothek rausgeschmissen, weil sie zu laut war.
She was kicked out of the library because she was too loud.
to dismiss / discharge
'entlassen' and 'rausschmeißen' can both mean that someone has to leave or loses their job. 'entlassen' is more neutral and fits official situations, for example in a company, hospital, or institution. 'rausschmeißen' is colloquial and sounds much harsher. It often emphasizes that someone has to leave against their will, sometimes because of bad behavior. In formal texts or conversations, it is better to use 'entlassen'. Among friends, 'rausschmeißen' can sound natural, but it comes across as rough.

Der Wirt hat den lauten Gast aus dem Lokal rausgeschmissen.
The landlord kicked the noisy guest out of the pub.
Nach zehn Jahren wurde Herr Kaya aus wirtschaftlichen Gründen entlassen.
After ten years, Mr. Kaya was dismissed for economic reasons.