One particular server setting to check, if your mail service is also your ISP (Internet Service Provider) is that you have "authentication" set for the outgoing mail server (i.e. the app is set to log in under your name when sending).
This is sometimes optional in the above scenario because when your phone is connected to WiFi, the mail server knows who you are (ah, this is one of our customers) from the address on the network connection.
And then on mobile data, it won't (know who you are).
Long press on the account -> account setup -> Manual -> Next and you'll be looking at detailed outgoing (sending) server settings. You do not want "do not login" under "authentication".