Normally when using IMAP or similar protocol for email, the client side directly reflects what is on the server side and vice versa.
Thus if you delete an email on the client, it automatically deletes the email on the server.
Depending on the client email app, some apps will give you the option of deleting an email off the phone while leaving it on the server for other devices to download.
Sounds like you need an email app with that feature. Unfortunately, I cannot help you pick one; the email app I use does not have that feature.