What can cause a sprained ankle to turn green and purple?

Brusing: The normal process by which a bruise heals is through the reabsorption of the hemoglobin from the injury. The varying colors is the breakdown of heme, which is the part of the red blood cells that carry iron. The colorations are the varying degrees of iron in the tissues from the injury. Time will only allow it to heal. Warm compresses increase circulation, which may help.

Ecchymosis.: Ecchymosis is the medical term for "black and blue". Purple and green are common as well, as the used blood by-products rise to the skin. It will go away over several weeks.