Can I unwarp my cutting board?
Impractical? I think the wet grass + sun idea sounds fantastic!
I see two options here-

Wood is shaped with the application of moisture and heat. Run it through some steam in the dishwasher and while it is still piping hot clamp it tightly between rigid boards to dry. This method works with all kind of wood shaping but you should know that there is always the risk that the stress will cause the board to crack while it dries.
For descriptions of this technique google &quot;wood steam bending&quot;. Most results will describe using a specialized steaming chamber rather than a dishwasher but the technique is the same.

The other method is mechanical: use a belt sander or planer to remove the convex material. Less risk but more work.