Either cut the good parts off and do lots of cutting on them in an effort to save your new big mat.
If it's not too terribly warped (and maybe if it is) you can always try to use contact cement to glue it to a smooth board. You apply the cement to both the board and the mat, then put them together. It may take a couple of people to get it smooth. You'll also need weight to hold it down while it cures.