Email uses connections to 2 mail servers, one for incoming and the other for outgoing mail. It sounds like the outgoing mail server (“SMTP” server) is not configured correctly. The most common error is not providing a user ID and password for the outgoing server when setting up the email account. It is slightly confusing because those fields are labeled “optional”, but they are only optional if you don’t want to send mail. It works at home because the Spectrum mail server knows you are a “trusted” user because you are logged in to their Wi-Fi network. When you are away from home you are not using their Wi-Fi, so it doesn’t “trust” you.
Enough for the explanation; here’s how to fix it:
The easiest way is to delete the Spectrum email account, then set it up again following the guidance on their website for iPhone setup. Go to Settings/Mail/Accounts and tap on the account to manage it.
You can also go to the same place, tap on the account, then tap on Outgoing (SMTP) server and entering your email ID and password.