abschleppen
to tow away
To pull a vehicle that is no longer roadworthy to another place with another vehicle, usually to a repair shop.
Mein Auto hatte eine Panne und musste abgeschleppt werden.
My car broke down and had to be towed away.

to tow away / pick up
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to tow away
To pull a vehicle that is no longer roadworthy to another place with another vehicle, usually to a repair shop.
Mein Auto hatte eine Panne und musste abgeschleppt werden.
My car broke down and had to be towed away.

'Abschleppen' (to tow away / pick up) is a separable verb. The prefix 'ab-' comes at the end of the main clause; in subordinate clauses the verb stays together, and in the infinitive with 'zu', 'zu' comes between 'ab' and 'schleppen'.
Der Pannendienst schleppt das kaputte Auto ab.
The breakdown service tows the broken-down car away.
The verb consists of the prefix 'ab-' and the base verb 'schleppen' (to drag or carry something heavy). The prefix reinforces the idea of transporting away or removing, which can be recognized in all meanings.
Wir mussten die alten Möbel aus dem Keller schleppen.
We had to carry the old furniture out of the basement.
When it is about vehicles, 'abschleppen' (to tow away) is often combined with places or reasons. Typical phrases are 'in die Werkstatt abschleppen' (to tow to the repair shop), 'von der Autobahn abschleppen' (to tow off the highway), or 'wegen Falschparkens abschleppen' (to tow away for illegal parking).
Das falsch geparkte Auto wurde abgeschleppt.
The illegally parked car was towed away.
This meaning is used exclusively in informal colloquial language. You would not use this expression in formal contexts.
Auf der Party hat er versucht, eine Frau abzuschleppen.
At the party, he tried to pick up a woman.
In the meaning 'sich abmühen' (to struggle), the verb is always used reflexively with 'sich' and the preposition 'mit' + dative. The structure is: 'sich mit etwas (Schwerem) abschleppen' (to lug something heavy around / to struggle carrying something heavy).
Sie hat sich mit den schweren Koffern zum Bahnhof abgeschleppt.
She lugged the heavy suitcases to the train station.
to pull / move
'ziehen' and 'abschleppen' have in common that something is moved by force. 'ziehen' is very general: you can pull a door, a suitcase, or a cart. 'abschleppen' is much more specific. It is used mainly when a vehicle can no longer drive or is parked illegally and is pulled away by another vehicle. The words can be confused because towing really does involve pulling. But not every kind of pulling is 'abschleppen'. For normal objects, use 'ziehen'; for a car that is being taken away, 'abschleppen' is appropriate.

Nach der Panne schleppt der Abschleppdienst das Auto in die Werkstatt ab.
After the breakdown, the towing service tows the car to the repair shop.
Der Hund zieht so stark an der Leine, dass Tom langsamer gehen muss.
The dog pulls so hard on the leash that Tom has to walk more slowly.