I would try white vinegar mixed with the soapy water.
If that does not work it may be time to accept it as patina! In which case the more the better. Serve more cheese, add more patina.

Although it's found in the laundry soap aisle, I've found Amaze will do just that when it comes to removing oily and greasy residue. As a chef I often bring home antique kitchenware or even Metro shelving that just needs a good but tedious cleaning. Amaze is an active enzyme so a soaking in a tablespoon or so in warm water works wonders. On the Metro shelving (and actually baking and oven racks too) I make a really sudsy batch, give the shelving a loose bath and spray with the garden hose. Works like a charm. Of course it's made for laundry so if it works on diapers, it's great on linens as well. I've even washed antique wood bowls for a good cleaning. Cheap and great results.

Your cheese board is dishwasher safe. Slate is non-porous, so don't worry about cleaners "soaking" into it.

Slate is porous and that's why the greasy stains are on the board. The grease from the cheese has actually soaked into the slate.

So -- To clean it, use a brush (like a nail brush) and dish washing liquid. That will probably not remove the stains completely. They will, however, over time, migrate into/across the stone, and seem less noticeable.

Then, another time, put something under the cheese when you serve it -- like either paper or real leaves. Just choose the leaves judiciously so you don't poison your guests or change the taste of the cheese. No oleander, please! 8-)

Well guys,
I used to use OxyClean on my slate kitchen floors!
Worked great.
Mix with hot water and soak your cheese board in it.
Or just pour it on and leave it in the sink for a while.
My floors would bubble up with the oxyclean "eating" the proteins etc on the floor.
Cheers
irina

Why not oil (and then wash) the entire board so you don't have "splotches" of oil, but a smooth sheen instead?

I agree with Keltrue-
You should oil your slate with mineral oil, your slate is thirsty and will absorb any oils from any cheeses you put on it. A well oiled board won't be so thirsty and you won't have the problem in the future.

Brooklyn Slate company makes cheeseboards and sells mineral oil to go with them

According to Brooklyn Slate's website, slate is dishwasher safe. I run mine all the time and it works great. (They also say slate is nonporous.)

http://www.brooklynslate.com/products/slate-cheese-board

You guys are great! Thanks, I think I will oil it- I didn't realize that the Brooklyn Slate Company sells it with mineral oil- I have that at home for my wooden boards. I have already tried soaking it with vinegar and scrubbing it with liquid soap to no avail. But I worry a bit about the cheese oils and the sanitary factor, and I don't have a dishwasher. I will try Amaze and Oxyclean. Thanks again! xo

Ditto Tuxedo and Keltrue --

If the slate is properly oiled with mineral oil, it won't absorb cheese oil.

I would be more concerned with cleaning an absorbent surface such as slate, meant for serving food, with something like Amaze or Oxyclean. It's one thing to clean shelving or floors with those products, but to clean an absorbent surface you eat off of with them? Err, no.

Clean the slate with very hot water and soap, and then oil it with food-grade mineral oil from the drug store.

Just saw on the Brooklyn Slate site that their boards are dishwasher safe -- if you are so worried about the oil stain from a hygiene perspective, then just run the slate through the dishwasher. Then you can rest assured that it has been treated adequately with heat.

You could always just cover it with cheese paper for serving.

Truly, it boggles the brain how many post without reading. Having no dishwasher pretty much removes that as an option, dontcha think? I had to see for myself that Brooklyn Slate actually makes the claim that slate is nonporous. Yep, they really do. And they are really wrong. Slate has an extremely low water absorption index which is why is it suitable roofing material but it IS porous, consequently the oil stains from the cheese. (i.e. PROOF) Yet another brain-boggler: why would BS sell it with mineral oil while simultaneously claiming it is nonporous? Makes zero sense (and calls into question BS's credibility, imho). As someone mentioned, your slate cheese board will develop a lovely patina given time. In the meantime, if the stains bug you, treat it with mineral oil. A little goes a long way.

All that said, I gotta toss in a chuckle at all the germophobes here. Y'all do know you're cuting you're cheese on consolidated dirt, right? *snort*

what discerning said, squared ... especially re all the advice to use non-food safe cleaners on -- which will also mean in, given slate's porous nature -- anything coming into direct contact with food. the cleaners are far more likely to cause illness, not to mention off-flavors, than any residual oil from the cheeses served from the slate. what's happened to our collective power of critical reasoning??

I almost feel like maybe TheKitchn should delete the comments about putting non-food-grade chemical cleaners on a porous surface that one would eat off of!!!! This seems like a question for an expert, rather than people who have cleaned their slate floors therefore slate cheese boards are the exact same situation....

"what's happened to our collective power of critical reasoning??"

(that bit of Wisdom bears repeating...food for thought)

I posted the suggestion earlier about oiling the board (which I still think is the best option)... I'm curious if you'll still be able to use chalk to write on it once it's "sealed" (if you even did that to label cheeses in the first place...). Let us know?

O.K. I know the O.P. doesn't have a dishwasher, but thanks to those who suggested it. Without this thread I would have been stuffed. I have tried washing/scrubbing/soaking including any combination you might think of using general household cleaners and oils and still ended up with crappy looking slate place mats and coasters. I just assumed they couldn't be done in there as they are natural and didn't even consider it. It works a treat. Thanks again!