Lay a straight edge across the cup and measure the gap at it's deepest, though remember the cup will be on both sides, so you'll lose double that measurement (as mentioned above). Unless it's a guitar with a Floyd Rose/Trem or you are trying to exactly copy something it won't matter having the body a few mm thinner. I make all my bodies 1.5" thick anyway unless I'm doing either of the above, so you should have enough material even with a thin top. Unless we are talking an extreme cup, in which case just buy a new blank.
I have flattened cupped bodies by clamping and moisture with limited success, but it is a big headache and there is always a very good chance it'll just cup again. These were in cases where too much work had already been done to stop, so I needed to save them. In your case I'd either plane it or just buy a new blank. It may sound extreme but if that cup comes back halfway through work or during finishing it will ruin your day/week!