If the target spell is an illegal target as Counterpoint tries to resolve, it won’t resolve and none of its effects will happen.

Alternatively, if the target spell is still a legal target but can’t be countered, Counterpoint will still resolve and allow you to cast a spell from your graveyard with mana value less than or equal to the target spell’s mana value.

If you cast a spell “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, those must be paid to cast the spell.

You cast the card from your graveyard as Counterpoint resolves. You can’t wait to cast it later in the turn. Timing restrictions based on the card’s types are ignored.

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

If the target spell has {X} in its mana cost, use the value chosen for X when determining that spell’s mana value.