MTG- do multi colored magic spells take on the spell color of every type of converted mana used?

For instance if i had a card (like the retaliator griffin) that cost a green a white and a red to put out, and another player tries to play an ability which gives him life for red spells being played, does retaliator griffin become a red spell because a red mana had to be used to bring it onto the battlefield? or are gold cards mutually exclusive to all other colors?