Cleaning nail polish from natural stone surfaces is not nearly as terrifying as it sounds--the nail polish binds and drys quickly, eliminating the chance of the dyes soaking into the stone and permanently staining it. Still, it's best to remove the nail polish from the stone as soon as possible after the initial spill. If the natural stone surface is rough, the stain will be much harder to remove once the polish dries, so make sure to clean up any rough stone surface spills immediately.
Use a butter knife to chip away any larger piles of the dried nail polish. Don't scrape so much that you damage the stone surface, just use the knife on globs that can be easily removed with a little force. If you notice the polish flaking, encourage the dry removal with leverage by sticking the butter knife underneath the flake and pulling it up.
Soak a rag or cloth in acetone. Hold the cloth over the stain and press down. Wait for about thirty seconds; then lift to see if the polish has returned to its liquid form. If it hasn't, leave the wet cloth over the stain for another minute.
Wipe away the liquified polish, making sure to wipe in a sideward motion (without spreading the stain) so that you aren't rubbing the nail polish into the natural stone surface. Once the excess polish has been removed, use a clean spot on the same rag to gently scrub away at any part of the stain that is left over, using more acetone if necessary.