One mechanical theme for some of the blue creatures in Innistrad is that you need to exile one or more creature cards from your graveyard as an additional cost. Examples of cards with this ability are Makeshift Mauler, Stitched Drake and Skaab Goliath.
As this is an additional cost, it is paid when you pay all costs when casting the spell. If you do not have any creature cards in your graveyard, you cannot pay this cost or cast the spell.
If one of these spells is countered, no costs are refunded. In other words, the exiled creature card will remain exiled even if the spell does not resolve.
Finally, all costs are paid when you cast the spell. As no one receives priority during the announcement of a spell or ability, an opponent cannot respond by removing a creature card from your graveyard to prevent you from casting the spell. For example, if you announce a Makeshift Mauler and only have one creature card in your graveyard, your opponent cannot cast and resolve Purify the Grave to prevent you from completing the casting process. In order to prevent you from exiling this card as part of the additional cost, he would need to remove the creature card from your graveyard before you began to cast the spell.