der Schnitt
cut
An injury or opening in a material caused by cutting.
Er hat sich beim Kochen einen tiefen Schnitt in den Finger zugefügt.
He gave himself a deep cut on his finger while cooking.

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cut
An injury or opening in a material caused by cutting.
Er hat sich beim Kochen einen tiefen Schnitt in den Finger zugefügt.
He gave himself a deep cut on his finger while cooking.

'Der Schnitt' (the cut) is the noun form of the verb 'schneiden' (to cut). Almost all meanings of the noun can be traced back to the action of cutting.
Das Messer macht einen sauberen Schnitt.
The knife makes a clean cut.
The expression 'im Schnitt' (on average) means 'durchschnittlich' (average/on average) and is a fixed phrase. It usually appears at the beginning or in the middle of a sentence.
Im Schnitt fahre ich jeden Tag 30 Minuten zur Arbeit.
On average, I commute 30 minutes to work every day.
The context makes the meaning clear. Words like 'Finger' (finger) or 'Wunde' (wound) point to an injury, 'Hose' (pants) or 'Haare' (hair) to style, 'Film' to video editing, and 'durch' (through) often to a cross-section.
Der Schnitt durch den Apfel zeigte, dass er innen faul war.
The cross-section through the apple showed that it was rotten inside.
To specify the meaning of 'style', 'Schnitt' (cut) is often used in compound words. The most common are 'der Haarschnitt' (haircut) and 'der Kleiderschnitt' (clothing cut/pattern).
Dein neuer Haarschnitt steht dir ausgezeichnet.
Your new haircut suits you extremely well.
When referring to an injury, 'Schnitt' (cut) is often used with verbs like 'sich zufügen' (to inflict on oneself) or 'behandeln' (to treat). Typical adjectives are 'tief' (deep), 'klein' (small), or 'oberflächlich' (superficial).
Der Arzt musste den tiefen Schnitt nähen.
The doctor had to stitch the deep cut.
The meanings 'film editing' and 'cross-section' often belong to a technical context. You find them in the film industry, in architecture, or in the natural sciences.
Für den Schnitt des Werbespots wurde eine Agentur beauftragt.
An agency was hired for the editing of the commercial.
seat / headquarters
'der Sitz' and 'der Schnitt' can both be important with clothing. 'der Sitz' describes how a piece of clothing sits on the body: it can fit well, loosely, or too tightly. 'der Schnitt' describes how the garment is made or cut, that is, its shape and style. The words can be confused because a good cut often leads to a good fit. Still, the focus is different: 'Schnitt' means the shape of the garment, while 'Sitz' means the result on the body.

Der Schnitt des Kleides ist modern, aber die Farbe gefällt mir nicht.
The cut of the dress is modern, but I don't like the color.
Bei der Anprobe achtet Lena vor allem auf den Sitz der Jacke.
At the fitting, Lena pays attention above all to the fit of the jacket.