abhauen
to run off
Colloquial for leaving a place quickly and often secretly; to run away or flee.
Als die Polizei eintraf, sind die Jugendlichen sofort abgehauen.
When the police arrived, the teenagers ran off immediately.

to run off / chop off
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to run off
Colloquial for leaving a place quickly and often secretly; to run away or flee.
Als die Polizei eintraf, sind die Jugendlichen sofort abgehauen.
When the police arrived, the teenagers ran off immediately.

'Abhauen' (to run off/to chop off) is a separable verb. The prefix 'ab-' comes at the end in main clauses. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er haut heute Abend früher von der Arbeit ab.
He's leaving work early this evening.
The auxiliary verb in the perfect tense depends on the meaning. For 'weglaufen' (to run away), a movement, 'sein' is used. For 'abtrennen' (to cut off/separate), an action with an object, 'haben' is used.
Der Hund ist gestern schon wieder abgehauen.
The dog ran off again yesterday.
In the meaning 'weglaufen' (to run away), 'abhauen' is very colloquial. It is used among friends or in informal situations.
Lass uns von dieser langweiligen Party abhauen.
Let's get out of this boring party.
The command 'Hau ab!' (Get lost!) is a very direct and impolite demand to disappear. It is often used out of anger or annoyance.
Hau ab und lass mich endlich in Ruhe!
Get lost and finally leave me alone!
to stay / remain
'bleiben' and 'abhauen' are opposites here because both have to do with a place. 'bleiben' means that you are in that place and do not leave. 'abhauen' means that you leave quickly or run off, often secretly or without properly saying goodbye. 'abhauen' is colloquial and often sounds somewhat negative or sudden. In a neutral situation, you would more likely say 'gehen' or 'weggehen', but the clear opposite of 'bleiben' is: 'bleiben' means being there, 'abhauen' means being gone quickly.

Der Gast haut einfach ab, ohne die Rechnung zu bezahlen.
The guest just runs off without paying the bill.
Wir bleiben heute im Garten, weil das Wetter so schön ist.
We're staying in the garden today because the weather is so nice.