schleudern
to hurl
To throw something with great force and speed.
Er schleuderte den Stein wütend gegen die Wand.
He angrily hurled the stone against the wall.

to hurl / to skid / to spin
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to hurl
To throw something with great force and speed.
Er schleuderte den Stein wütend gegen die Wand.
He angrily hurled the stone against the wall.

The verb 'schleudern' (to hurl) is related to the noun 'die Schleuder' (slingshot). The idea that something is moved powerfully and quickly with a slingshot helps you understand the basic meaning of throwing.
Die Maschine schleudert kleine Teile mit hoher Geschwindigkeit aus.
The machine ejects small parts at high speed.
In connection with vehicles, the fixed expression 'ins Schleudern kommen' or 'ins Schleudern geraten' is used very frequently. This is often more natural than using the verb 'schleudern' alone.
Auf der nassen Straße geriet der Wagen plötzlich ins Schleudern.
On the wet road, the car suddenly started skidding.
This meaning is relevant only in the context of laundry and washing machines. Signal words like 'Wäsche' (laundry), 'Waschmaschine' (washing machine), 'nass' (wet), or 'Umdrehungen' (revolutions) make it clear that removing water is meant.
Du kannst die Handtücher bei 1400 Umdrehungen schleudern.
You can spin the towels at 1400 rpm.
The meaning 'billig verkaufen' (to sell cheaply) is colloquial. The separable particle 'raus-' is often added here: 'etwas rausschleudern' (to sell something off).
Zum Saisonende schleudert das Geschäft die restlichen Winterjacken raus.
At the end of the season, the store is selling off the remaining winter jackets.
to throw
'werfen' and 'schleudern' both mean moving something through the air with your hand or arm. 'werfen' is the normal, general word. You can 'werfen' a ball, a key, or a stone. 'schleudern' sounds stronger: it means that something is thrown with great force and often very quickly. That is why 'schleudern' fits especially when the movement seems violent, dangerous, or uncontrolled. As a simple rule: anyone can 'werfen' a ball, but someone who 'schleudert' something uses a lot of force.

Vor Wut schleuderte er den kaputten Stift in den Papierkorb.
In anger, he hurled the broken pen into the trash can.
Du hast den Ball am Montag weit über den Zaun geworfen.
On Monday, you threw the ball far over the fence.