The only way to "mass delete" things is to go into the game's data folder in File Explorer and start deleting things. The folder you'll need is C:\Users\yourUsername\AppData\LocalLow\Jundroo\SimplePlanes\AircraftDesigns. Don't delete anything with an underscore in front of the name (those are all used by the AI for challenges/races), but other than that you should be able to delete anything you want. (There's a "Restore Stock Planes" button in the main menu - I think under Settings - in case you accidentally delete those too.)

If you're on iOS, or (probably) Android or Mac, I'm afraid you're out of luck since I don't think you can access the appropriate folder using their respective file navigation tools. You'd have to delete them one at a time in-game.