If you pay the casualty cost of a spell, the copy will resolve before the original spell.

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

The copy of the spell is created on the stack, so it's not “cast.” Abilities that trigger when a player casts a spell won't trigger.

You may sacrifice only one creature to pay a spell's casualty cost, and you copy the spell only once.

Casualty N means “As an additional cost to cast this spell, you may sacrifice a creature with power N or greater.” and “When you cast this spell, if a casualty cost was paid for it, copy it. If the spell has any targets, you may choose new targets for the copy.”

If a spell has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.