Does a replacement effect that exiles a creature instead of destroying it prevent a dies trigger from going on the stack?

A 'dies' trigger uses the specific game term 'dies,' which is defined in CR 700.4 as a creature being put into a graveyard from the battlefield. If a replacement effect instead sends the creature to exile, the creature never reaches the graveyard from the battlefield, so the condition for the trigger is never met.

Replacement effects (CR 614.1) modify events as they happen — they don't let the original event occur and then change it afterward. So if an effect says 'If a creature would be destroyed, exile it instead,' the destruction event is replaced entirely by an exile event. The creature goes from battlefield to exile, not from battlefield to graveyard.

Because the creature never enters the graveyard, it never 'dies' by the game's definition (CR 700.4). Any ability that triggers 'when [this creature] dies' or 'whenever a creature dies' checks whether the event that occurred was a creature moving from the battlefield to the graveyard — and since it wasn't, the trigger condition is never satisfied and nothing goes on the stack (CR 603.2).

Concrete example: Your opponent controls Teysa Karlov and you have a creature with 'When this creature dies, draw a card.' If you use Leyline of the Void's replacement effect so that creature would be exiled instead of going to the graveyard when it dies, the creature goes to exile. It never 'dies,' so the draw trigger never triggers, and Teysa's doubling ability is also irrelevant.

Note: If a creature is sacrificed or dies for any other reason and a replacement effect redirects it to exile, the same logic applies — the 'dies' trigger condition is not met regardless of why the creature was leaving the battlefield.