It won't dilute with water, and some sort of petroleum solvent would be needed to thin it, like mineral spirits, etc. Then it's not food-safe anymore, and perhaps even toxic in other ways (inhalation hazard, thru-skin absorption, etc) with a solvent added.
Mineral oil really isn't that expensive anyway. If cost is a concern, the laxative-grade stuff is likely the least expensive. I get it in 16 oz. bottles for ~ $1.98 at Walmart, for example. And even the pricier stuff, like the Norton oil, goes a pretty long way on a per-use basis. If used on stones that don't really drink up a lot of it, it goes even further. The 'food-safe' stuff is worth every penny, when you think about it. Unless one DRINKS it outright, it's otherwise completely inert and harmless, and it solves a lot of issues in sharpening.
Some synthetic oil stones will drink a lot of oil, if they're not pre-filled with oil/grease from the factory. Of these types that I use, I keep them stored in a sealed bin filled with the 'cheap' laxative-grade mineral oil, to help minimize their 'thirst' for the stuff when I'm using them. Then, when I need to add a little oil during use, I can drizzle a little bit of my better oil (Norton & others) on the stone, without feeling compelled to completely fill the stone with it. That helps to stretch the life of my better oil.