For the sake of emphasis, is it possible to write: "The larger the area of forest is destroyed, the more frequent are natural disasters"?
The first "is" is definitely incorrect - delete it. What about "As larger areas of forest are destroyed, natural disasters become more frequent"? It could be improved by eliminating the passive voice in the introductory clause, but I don't know your subject. For example, "As man destroys larger areas of forest, natural disasters become more frequent."