Wooden cutting board turns black
The black spots can be one of several things, but are likely a variety of mold. Black stains can also be caused by a reaction to the iron in your knives (particularly if you use carbon steel blades instead of stainless steel). If it is mold, it is growing because even though the surface of your cutting board is dry, moisture has soaked in, probably because it needs to be oiled or waxed.

To recondition a butcher block or cutting board that is stained or gouged, you can sand the surface down, and reoil.


Use a sanding block to keep the surface from getting wavy as you sand.
Start sanding with 120 grit (80 if you are removing big gouges), and sand evenly, moving with the grain, until the stains are gone, or almost gone (if a few very deep ones survive, don't worry about it).
Repeat the sanding with 240, then 400 grit until the roughness from the previous sanding is gone.
Reoil with any Butcher Block Conditioner. There are many out there, and they are either food-safe mineral oil, or that oil with a few other waxes mixed in. Many are good, but my favorite is Howard's Butcher Block Conditioner. Follow the instructions, but it will amount to making a liberal application, allowing it to sit for a while, then wiping off the excess.
Maintain the new surface by drying the cutting board well before storing (as you are already doing), and wiping lightly with mineral oil briefly every few times you use it, much like maintaining a cast iron pan.