Reinstall mail without restoring messages

You need to understand that to install the Mail app you will have to reinstall the operating system. I don't think that is what you want to do, however. What you can do is to delete the account in Mail and then create a new account and then set it up. Keep in mind that any messages you want to save must first be saved to a Local folder or they will be lost with the account deletion.

What kind of email accounts?

If it is POP, remove my the account will erase all of them. Adding it back will only get new messages.

If it is IMAP, you will have to erase all of the messages on the server.