Mail app. damaged, losing all my email
Any email you have stored on your Mac from your Mail app is located in your user account's library folder. More specifically, in macOS Sierra you can access your mail data as follows:


Make sure you're in the Finder
Press and hold the option key
Click on the Go menu and select Library
Your user account's Library folder will open (you can now let go of the option key) 
Within this folder is located a Mail folder. This contains any Mail data actually stored on your Mac.


Now, assuming you have Time Machine backups, all of this should already be backed up. However, if you don't, then you could copy this Mail folder onto a couple of USB drives for safe keeping until you sort out your Mail app issue.

NOTE: It's not clear from your question how you upgraded to macOS Sierra, nor what type of email account you have. As a result, we cannot advise how much data, if any, you have in your Mail folder.