Does Leyline of the Void stop graveyard triggers from happening before exiling the card?

Leyline of the Void has a replacement effect: instead of a card going to an opponent's graveyard, it is exiled. Because this is a replacement effect, the card never actually reaches the graveyard at all — it goes directly to exile instead (CR 614.1). There is no intermediate moment where the card exists in the graveyard for triggers to see.

Triggered abilities that look for a creature 'dying' or being 'put into a graveyard' (e.g., 'when this creature dies, do X') require the card to actually enter the graveyard to trigger (CR 700.4, CR 603.6a). Since Leyline's replacement effect diverts the card to exile before it ever touches the graveyard, those triggers never have the event they need and simply do not trigger.

This is different from a triggered ability that exiles a card from the graveyard — that would require the card to have already arrived there. Leyline's replacement happens earlier, at the moment the card would be placed into the graveyard (CR 614.6).

Concrete example: Your opponent's Bloodghast is dealt lethal damage. Normally, Bloodghast would die and its 'whenever Bloodghast is put into a graveyard from the battlefield' trigger would go on the stack. With Leyline of the Void in play, Bloodghast is exiled instead of entering the graveyard, so the trigger condition is never met and the ability never triggers.

Note: 'Leaves-the-battlefield' triggers on the dying permanent itself or on other permanents watching for it still fire because the creature did leave the battlefield — but abilities specifically requiring placement into the graveyard do not (CR 603.6a).