If you cast Grisly Sigil targeting a creature or planeswalker that hasn't been dealt noncombat damage this turn, choose to pay its casualty cost, and choose not to change the target, the copy will deal 1 damage and you will gain 1 life. Then, the original spell will resolve. It will deal 3 damage, and you will gain 3 life.

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.”

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.

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

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