Cut Your Losses

Casualty 2 (As you cast this spell, you may sacrifice a creature with power 2 or greater. When you do, copy this spell and you may choose a new target for the copy.)
Target player mills half their library, rounded down.

Magic Online Promos

Streets of New Capenna

Casualty 2
Target player mills half their library, rounded down.

Streets of New Capenna Promos

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 you cast Cut Your Losses and copy it targeting the same player, that player will mill half their library, then mill half of what remains after that. They do not mill their entire library.

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

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.