You must have an internet connection to send and receive email.
If you have a rooted phone, you could use a firewall program (Droidwall, Avast Mobile Security, etc.) to block certain apps from accessing the internet. In this case, you could create a whitelist and only allow email app to access. However, you'd need to leave your internet connection enabled. This would save on data usage, but likely not really save on battery consumption in a significant way.
If the reason to disable internet is to save on battery, there are apps which will turn on the internet connection occasionally to check for new messages, and then turn off again. This limits the amount of time you are online which saves some battery. I use Tasker to do this, but there are other simpler apps out there.
Finally, check your account and sync settings to ensure you don't have other unwanted things set to sync on your phone.
