Installing it again would work but takes time and is absolutely not needed. Warcraft III and Warcraft III:TFT both being games that were able to be played offline, they have local campaign content and save. Which means they don't have cloud-like data such as Starcraft 2. With this in mind you can assume there is, somewhere in your installation, those saved games you want to get rid of. You can delete (or maybe just backup for latter) them. Find your Warcraft 3 profile, your in-game local name for your campain, and delete it! Also, you can just start another one. Being binded to directories, the game wont let you have the same name.
Have fun playing this super game again!