I'm not sure if there's a mass-delete when using the app. You can delete entire "pages" of emails in the Gmail web interface.
As for deleting from the app but not from the server, that really depends on what mail service you're using. If you're on Gmail or your email is set up as IMAP mail, that's pretty much a direct connection and it will sync the deletions. If you're on POP3, you can have it set up to delete the messages locally but keep them on the server, this is a setting within the email server setup in your mail client.