If Spirit Script becomes a copy of a card and then leaves the graveyard, it will stop being a copy of the card. However, if it left the graveyard due to an ability allowing you to cast it (such as flashback or recite) it will keep that ability.
If an effect moves a Spirit Script that is copying a card from your graveyard and then asks for characteristics of that card (for example: Exile target card from a graveyard. If it was an instant, draw a card.) it will use the characteristics of the card Spirit Script was copying.