Rust stain, food stain, red wine stains, blood stain, urine stains, etc, are nearly impossible to remove from marble and natural stone floors. Strong acidic cleaning product might provide some results but it could also damage the tile as well.
Try Faber Oxidant right now and remove most types of stains from marble, travertine & terrazzo. This product is easy to use, provides results fast and it will not affect the stone in a negative way. Just apply it on the stain, allow to work, light scrub and repeat the operation for heavy duty stains.