What is the best way to clean a sisal rug to remove stains from it?

You need an organic cleaner from the pet store. These clean up anything organic, such as the spilled drinks and pet stains. Get one that is safe for a sisal rug.

How big is the rug, and what kind of drinks. Red wine might be permanent, but other drinks (except those with milk or whipped cream) might come out with just a little vinegar mixed with water. If the rug is small enough to carry outside, lay it on the driveway and use the hose to rinse clean. I get pet stains out with enzymatic cleaners that you can buy in stores or online. Before you do anything, test an area to make sure the rug can handle being wet. If the rug is already compromised, I would try, in this order: plain water, then water with a little white vinegar (especially on pet stains). Then I would try a little commercial carpet cleaner diluted in in water. Let the rug dry in between and see if you notice a difference. If not, I would try water with some oxygen bleach powder well dissolved in it, then water with a little chlorine bleach. (this last one may well make the situation worse, so test small areas). Good luck

https://www.hunker.com/13423103/how-to-get-stains-out-of-sisal-rugs

See if this link helps.

http://www.uniquecarpetsltd.com/sisal-maintenance

I recommend sprinkling on some Baking Soda. Then make a solution with Hydrogen Peroxide and a couple drops of dish soap. Let it set a while then blot it back up with rags. This process should work on your sisal rug just fine.

Steam clean it?