verziehen
to move away
To change one's place of residence; to move to another place.
Unsere ehemaligen Nachbarn sind letztes Jahr nach Hamburg verzogen.
Our former neighbors moved away to Hamburg last year.

to move away / spoil / warp
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to move away
To change one's place of residence; to move to another place.
Unsere ehemaligen Nachbarn sind letztes Jahr nach Hamburg verzogen.
Our former neighbors moved away to Hamburg last year.

'Verziehen' is an inseparable verb based on the base verb 'ziehen' (to pull). The prefix 'ver-' remains firmly attached to the stem in all conjugated forms and sentence positions.
Meine Tante ist vor langer Zeit nach Kanada verzogen.
My aunt moved away to Canada a long time ago.
You can recognize the meaning of 'verziehen' from the sentence structure. With the auxiliary verb 'sein' (to be), it means 'to move away'. As a transitive verb with a person as the object, it means 'to spoil'. Reflexively ('sich verziehen') it can mean 'to deform/warp' (material) or, colloquially, 'to disappear/clear off' (person).
Sie sind letztes Jahr verzogen.
They moved away last year.
In the meaning 'to change one's place of residence', the perfect tense is always formed with the auxiliary verb 'sein' (to be). The reason is that it describes movement from one place to another.
Wann seid ihr in diese Wohnung verzogen?
When did you move into this apartment?
The expression 'das Gesicht verziehen' (to make a face) is a fixed collocation. It describes an involuntary reaction to pain, disgust, or something unpleasant. The object is almost always 'das Gesicht' (the face) or 'die Miene' (the expression).
Beim Anblick der Wunde verzog er das Gesicht.
At the sight of the wound, he made a face.
The reflexive form 'sich verziehen' in the sense of 'to go away' or 'to disappear' is colloquial. As a command in the imperative ('Verzieh dich!' — 'Get lost!'), it is a very rude way of forcing someone to leave.
Es wird spät, ich glaube, ich verziehe mich mal.
It's getting late; I think I'll clear off now.
to disappear
'verschwinden' and 'sich verziehen' can both mean that someone leaves a place. 'verschwinden' is more general: afterward, someone can no longer be seen, or you are roughly telling someone to leave. 'sich verziehen' is colloquial and often sounds dismissive or annoyed. It fits especially when someone leaves quickly and without much explanation. The words can be confused because they feel similar in sentences like 'Verschwinde!' (Get lost!) and 'Verzieh dich!' (Clear off!). However, 'Verzieh dich!' is very direct and rude; in neutral situations, 'weggehen' or 'verschwinden' is usually more natural.

Als der Chef ins Lager kam, verzogen sich die Kollegen schnell.
When the boss came into the warehouse, the colleagues quickly cleared off.
Der Junge verschwand in der Menge, bevor seine Mutter ihn rufen konnte.
The boy disappeared into the crowd before his mother could call him.