This depends on the depth of the cut. If it is just a shallow scratch, nothing will happen to your tattoo. If the cut is deep, there is a chance that the colors will fade and bleed out, but this is a rare occurrence. If this does happen, you can always get it touched up.

If it is a really deep cut, you probably have other problems to worry about than your tattoo, but when the healing is done, you still have the option of a touch up to repair any damage.