Looks like wool with an acrylic backing and acetate facing. In which case you should not wash it. Probably should have it dry cleaned, but if that's the only soil on it, you could try spot cleaning, but only if the backing is solid. If it's starting to flake or pull away from the wool, I wouldn't do even that. If you spot clean, use a dry-cleaning type fluid, or the stuff that comes with Dryel, or a cloth dampened (not wet!) with woolite and cold water and very, very lightly dab at the stain.
Does it show through to the front? If not, honestly, the only thing I personally would do with it is try to lighten that stain a bit--futzing with it too much could cause more of a problem than the stain does... If you can succeed in minimizing it, I wouldn't even try to get it up all the way....
After recently nearly ruining a gown trying to remove soil on the inside of it that didn't show on the outside, I say, less is often more.... I'd bet most of us have indeed ruined or made worse a garment from trying "too hard" to make it "perfect."