
sägen
to saw
To cut through or work on something, usually wood, metal, or plastic, with a saw.
Der Tischler sägte das Brett exakt auf die richtige Länge.
The carpenter sawed the board to exactly the right length.
to saw / snore
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to saw
To cut through or work on something, usually wood, metal, or plastic, with a saw.
Der Tischler sägte das Brett exakt auf die richtige Länge.
The carpenter sawed the board to exactly the right length.

to snore
Colloquial for snoring very loudly and noisily while sleeping.
Ich konnte kaum schlafen, weil mein Zimmernachbar die ganze Nacht gesägt hat.
I could hardly sleep because my roommate was snoring all night.

to undermine someone
A fixed expression meaning to work secretly and schemingly to push someone out of their position or office.
Man merkt deutlich, dass die ehrgeizige Kollegin am Stuhl ihres Chefs sägt.
You can clearly tell that the ambitious colleague is undermining her boss's position.
In its main meaning, 'sägen' (to saw) is often combined with materials that can be cut. Common objects are 'Holz' (wood), 'ein Brett' (a board), 'ein Ast' (a branch), or 'Metall' (metal).
Er hat den ganzen Nachmittag Holz für den Winter gesägt.
He sawed wood for the winter all afternoon.
The meaning 'laut schnarchen' (to snore loudly) is colloquial. It is used to describe the noise as very loud and disturbing, similar to the sound of a saw. The context is always sleeping.
Mein Hund hat letzte Nacht so laut gesägt, dass ich aufgewacht bin.
My dog snored so loudly last night that I woke up.
The idiom 'an jemandes Stuhl sägen' (to undermine someone's position) is a fixed construction with the preposition 'an' and the dative. It means that someone is trying to secretly weaken another person's position.
Er hat das Gefühl, dass sein neuer Kollege an seinem Stuhl sägt.
He has the feeling that his new colleague is undermining his position.
to snore
Schnarchen is the neutral term for loud breathing noises during sleep. Sägen is a colloquial, figurative term for this and often emphasizes that the snoring is especially loud and noisy. Schnarchen is appropriate in a factual statement, while in casual conversation sägen can express the stronger effect.

Mein Bruder sägt im Gästezimmer so laut, dass ich ihn durch die Wand höre.
My brother snores so loudly in the guest room that I can hear him through the wall.
Mein Bruder schnarcht im Gästezimmer so laut, dass ich ihn durch die Wand höre.
My brother snores so loudly in the guest room that I can hear him through the wall.