Open Gmail
Click the gear icon
Select See all settings
Go to the Accounts and Import tab
Under Send mail as, find the email address
Click delete or remove next to the email address
Confirm the removal
If needed, go to Accounts and Import
Under Check mail from other accounts, find the email address
Click delete or remove next to it
Confirm the removal
If the email address is your Google account address, you cannot remove it without deleting the Google account
If the email address is an alias, remove it from your Google Account settings
Save changes if prompted