I am not sure it is the same on Z2,but on Z1 if you go to settings and tap your email in the default email app,you get an option auto download attachments when connected to wifi.
The option alexdon describes is available in Z2 as well but you can only set this for attachments. There's no setting that stops the phone from checking email when not connected to WiFi. You can set the email account to manual under "Account check frequency" in the same menu and then only check your email when you have the WiFi icon.
