How to clean a whetstone?

If this is an oilstone (which is considered old fashioned exactly because of these issues), an oft-mentioned ultima ratio remedy is boiling it in soapy water. YMMV, this could destroy the stone. If you know what exact type (eg arkansas) your oilstone is, research instructions specific to that stone type.

If it is a waterstone, abrading the stone - with a flattening plate, diamond stone, another waterstone until unaffected material is brought to the surface is the recommended method.

My uncle used a dry stiff wire brush to remove crud, then dipped the brush into a pail of sudsy water and scrub it again. Then use a cloth with clean water (well wrung out), a dry up with a clean cloth, and a final dry wire brush on any remaining spots.

I think the best way to clean a old whetstone with lots of buildup would be to rub it on a flattening plate, which also has the advantage of flattening your whetstone.

On a whetstone for use with water you use a nagura stone. There are natural and artificial nagura, cheap ones and expensive ones. The nagura is harder than your whetstone. You rub it on your whetstone in between sharpening your knife whenever you feel the surface of your whetstone is loaded (clogged) with particles.

It abrases the surface of your stone, thus cleaning its surface while also creating the slurry, the mix of water and whetstone particles needed for a less aggressive, more regular sharpening of a knife.

Here’s a YouTube video of cleaning a stone and creating a slurry with a nagura.

While Bar Keepers Friend is a great cleaner with many uses, it is NOT great enough to clean an ultra-fine whetstone.

I use three grades of whetstone surfaces between two stones to do my sharpening jobs: Coarse, Fine, and Ultra-Fine. Coarse and Fine are on a single bastard stone, and Ultra-fine is a smaller dedicated stone.

The cleaning problem is presented by the ultra-fine whetstone; it remains clogged by particulates and discolored by impurities, the colors of which range from the expected shades of grey to suspicious sticky brown.

Boiling with detergents did not help. Lye (potassium hydroxide or sodium hydroxide) did. Two caveats: Do NOT allow it ANYWHERE near aluminum (it acts as does acid), and use VINEGAR (acetic acid) to neutralize it.

Lye works greatly on lots of things, especially when it comes to deposits involving extremes of heat and time, but it should be used with great care. The reasons why "excessive" bathing was generally regarded as unhealthy was understandable—considering people over a century ago were horribly ignorant regarding chemistry and physics. (nobody thought to bathe with vinegar after applying lye soap)