Can I delete gmail on my phone or computer at the same time?

Yes it does. Your Gmail is stored on Google's servers, it is not stored on your phone, on your computer, or on any other device from which you access it. If you delete an email using a mail client on your phone, it is deleted from Google's server and therefore will not appear on any device from which you access your Gmail.

Using Apple Mail app, if you delete an email message on your computer, it is deleted on your iPhone too (and viceversa)

Regards

Giulio

If you're talking about Gmail app, it's the same thing/behavior.

Regards

Giulio

If, after deleting an email message, you close the Gmail apps (on the computer and on your iPhone), then you re-open them, it should work.

+1

Giulio