Does Sacrifice Count as Dying Mtg?

Yes you can . Dying is a keyword that means going from the battlefield to the graveyard. This includes sacrifice.

What counts as dying in MTG?

Creatures die if they take lethal damage or have their toughness reduced in less than 1, as a State-based action. Planeswalker die if they have no loyalty counters on them. Both of them die if they get destroyed, or any other effect or spell that make them go from the battlefield to the graveyard, such as Sacrifice.

Does sacrifice count as damage MTG?

When one your creatures that is able to be sacrificed is dealt damage, can it be sacrificed as an instant and then no damage being dealt.