ausschlagen
to turn down
To reject or refuse an offer, request, or invitation.
Sie hat das Jobangebot ausgeschlagen, weil das Gehalt zu niedrig war.
She turned down the job offer because the salary was too low.

to turn down / to kick out / to sprout
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to turn down
To reject or refuse an offer, request, or invitation.
Sie hat das Jobangebot ausgeschlagen, weil das Gehalt zu niedrig war.
She turned down the job offer because the salary was too low.

'Ausschlagen' (to turn down / kick out / sprout) is a separable verb. In a main clause, the prefix 'aus' comes at the end; in a subordinate clause, the verb stays together; and in the infinitive with 'zu', 'zu' comes between 'aus' and 'schlagen'.
Das Pferd schlug plötzlich aus.
The horse suddenly kicked out.
The verb consists of the prefix 'aus-' and the verb 'schlagen' (to hit/strike). The basic meaning of 'schlagen' (to make a quick, forceful movement) is directed in different ways by 'aus-' (out, outward).
Im Frühling schlagen die Bäume wieder aus.
In spring, the trees sprout again.
When someone knocks something out of their own body (e.g. a tooth), a reflexive construction with the dative is used. The person to whom something happens is in the dative.
Er hat sich beim Sturz einen Zahn ausgeschlagen.
He knocked out a tooth in the fall.
In the meaning 'ablehnen' (to reject/turn down), 'ausschlagen' (to turn down) is often combined with things that are offered to you. Typical are: 'ein Angebot' (an offer), 'eine Einladung' (an invitation), 'eine Warnung' (a warning), or 'ein Erbe ausschlagen' (to disclaim/turn down an inheritance).
Er hat die Warnungen seiner Freunde einfach ausgeschlagen.
He simply ignored his friends' warnings.
You can recognize this meaning from the context of measuring devices. Words like 'Zeiger' (needle/pointer), 'Skala' (scale), 'Messgerät' (measuring device), or names of devices, e.g. 'EKG' (ECG) or 'Seismograph' (seismograph), clearly point to this usage.
Der Geigerzähler schlug in der Nähe des alten Labors aus.
The Geiger counter deflected near the old laboratory.
When 'ausschlagen' is used in connection with the body, it usually describes the sudden appearance of a skin rash. Here the verb is used without an object.
Meine Haut schlägt bei dieser Seife immer aus.
My skin always breaks out from this soap.
In this meaning, 'ausschlagen' (to kick out) is used almost exclusively for animals that kick with their hind legs. So the context is always an animal, usually a horse, donkey, or mule.
Der Esel schlug aus, als der Hund zu nahe kam.
The donkey kicked out when the dog came too close.
This meaning is typical of botany and nature. When the context is plants, trees, or buds growing in spring, this verb is appropriate.
Die Knospen an den Zweigen beginnen auszuschlagen.
The buds on the branches are beginning to sprout.
to step / kick
'treten' and 'ausschlagen' can both describe a movement with the foot or leg. 'treten' is the general word: a person or animal kicks against something or someone with their foot. 'ausschlagen' is more specific and is used here mainly for animals, especially horses. It means a sudden, forceful movement with the hind legs. For people, you normally say 'treten'. For a horse or another animal, 'ausschlagen' sounds more precise when the movement is sudden and dangerous.

Auf dem Hof schlug das Pferd plötzlich aus, als ein Hund zu nah kam.
In the yard, the horse suddenly kicked out when a dog came too close.
Beim Fußball trat Paul aus Versehen gegen das Bein seines Freundes.
During soccer, Paul accidentally kicked his friend's leg.