It of the Horrid Swarm

If you cast a spell for another cost “rather than paying its mana cost,” such as an emerge cost, you can’t choose to cast it for any other alternative costs. You can, however, pay additional costs, such as kicker costs. If the spell has any mandatory additional costs, those must be paid to cast it.

The mana value of a creature spell with emerge isn’t affected by whether its emerge cost is paid. For example, if you cast Decimator of the Provinces for its emerge cost and sacrifice a creature whose mana value is 3, Decimator of the Provinces’s mana value remains 10.

An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack without resolving.

Once you begin to cast a spell with emerge, no player may take actions until you’re done. Notably, opponents can’t try to remove the creature you wish to sacrifice.

If you sacrifice a creature with {X} in its mana cost, that X is 0.

The creature chosen to be sacrificed is still on the battlefield as the cost of the emerge spell is determined and as you activate mana abilities to cast the emerge spell. Its abilities may affect the spell’s cost, be activated to generate mana, and so on. However, if it has an ability that triggers when a spell is cast, it will have been sacrificed before that ability can trigger.