The best and easiest way to straighten a warped wooden cutting board is to turn it over so the part of the cutting board that was sitting on the counter is now exposed to the air.
Another way of looking at it is that a warped cutting board usually cups. You want the inside curve to be facing the counter. This way, the corners of the cutting board are resting on the counter, while the middle of the cutting board is arcing up and away from the counter.
This will allow the cutting board to dry evenly on both sides and will gradually straighten the warped cutting board.
The reason is that the cupping happens when the board dries unevenly causing the moisture on one side of the board to be different from the other side. Usually, the top dries faster than the bottom causing the board to cup upwards. If you flip the board then you’ll allow the bottom, or damp side, of the board to dry faster.
It may take a couple of days or a few weeks, but it’s the best and gentlest way to straighten a warped cutting board.