hochziehen
to pull up
To physically move or pull something upward.
Er zog die schwere Kiste mit einem Seil hoch.
He pulled the heavy box up with a rope.

to pull up / tease
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to pull up
To physically move or pull something upward.
Er zog die schwere Kiste mit einem Seil hoch.
He pulled the heavy box up with a rope.

'Hochziehen' (to pull up) is a separable verb. In main clauses, the prefix 'hoch' goes at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er zieht die schwere Tasche hoch.
He pulls the heavy bag up.
The verb consists of the direction 'hoch' (up) and the verb 'ziehen' (to pull). Most meanings can be derived from this basic idea of 'pulling upward', including the figurative ones.
Die Bauarbeiter ziehen die Mauer Stein für Stein hoch.
The construction workers are putting up the wall brick by brick.
The many meanings can often be distinguished by the object or the grammar. A physical object (box, flag), a building, a person ('jemanden'), a reflexive pronoun ('sich'), or 'die Nase' (the nose) point to the respective meaning.
Sie zog die Augenbrauen hoch. (Körperteil)
She raised her eyebrows. (body part)
When 'hochziehen' means 'necken' (to tease), it always needs a person in the accusative. An explanation often follows with 'mit' (dative) or 'wegen' (genitive/colloquially dative), naming the reason for the teasing.
Die Kollegen ziehen ihn immer mit seiner bunten Krawatte hoch.
The colleagues are always teasing him about his colorful tie.
In the meaning of 'sich nach oben bewegen' (to move upward), the verb is reflexive and is used with the preposition 'an' + dative. The structure is: 'sich an etwas (Dativ) hochziehen' (to pull oneself up on something).
Das Kind zog sich am Tisch hoch und machte seine ersten Schritte.
The child pulled itself up on the table and took its first steps.
When you say that someone 'hochzieht' (puts up) a building, this is a rather colloquial and vivid way of saying 'bauen' (to build) or 'errichten' (to erect). It often emphasizes speed or impressive height.
Die haben das neue Einkaufszentrum in nur einem Jahr hochgezogen.
They put up the new shopping center in just one year.
to build
'bauen' and 'hochziehen' can both mean that a building or a large structure is being built. 'bauen' is the neutral and general word. It works for almost any building and also for smaller constructions. 'hochziehen' sounds more figurative and often a bit more colloquial. It emphasizes that something is being built upward quickly or visibly, for example an apartment block or a hall. Learners may confuse the words because both fit when erecting buildings. 'bauen' is usually the safer choice; 'hochziehen' fits especially with large, tall, or quickly built buildings.

Am Bahnhof ziehen Arbeiter gerade ein neues Bürogebäude hoch.
At the train station, workers are currently putting up a new office building.
Die Familie baut ein neues Haus mit großem Garten.
The family is building a new house with a large garden.