When you destruct something, you destroy or wreck it. A developer might buy an old building in order to destruct it and build a shiny new one in its place.
The verb destruct isn't as common as its relatives, destructive, destruction, and self-destruct, but you can use it to mean "wipe out" or "destroy." Your doctor might worry that your lack of sleep and frequent soda drinking will destruct your health, and a kindergartner will probably wail in frustration if her little brother destructs her Lego creation. Destruct comes from destruction, most likely as 1950's US defense industry jargon.