Learn Turkish: Dudaklarını kanatasıya ısırdı. - He bit his lips until they bled.

The suffix -(y)AsIyA is added to a verb stem to show that an action reaches an extreme limit or continues to the point of a specific result. Here, it indicates the biting continued up to the extreme physical limit of causing blood. It translates well to 'until' or 'to the point of'.

Why is the verb root kanat- instead of just kana- (to bleed)?

Kanamak means 'to bleed' and is intransitive. Because the subject is acting upon a direct object (his lips), Turkish uses the causative verb kanatmak (to make bleed). Literally, this sentence means 'He bit his lips to the point of making them bleed.'

Why does dudaklarını have an accusative suffix if the bleeding is an adverbial condition?

The accusative suffix -ı on dudaklarını is triggered by the main verb ısırdı (bit), not by the converb kanatasıya. 'His lips' are the specific direct object of what he bit, while the converb simply acts as an adverb describing how intensely he bit them.

Could dudaklarını also mean 'your lips' in a different context?

Yes. Without a pronoun like onun (his/her) or senin (your), dudaklarını can be parsed as dudak-ları-n-ı (his/her lips + accusative) or dudak-ların-ı (your plural lips + accusative). We assume 'his own lips' based on logical context, but grammatically it is ambiguous without seeing the rest of the paragraph.