Welcome to Android Central! Which phone, and which email app are you using? Most email apps don't have a delete all option--the best you can do is activate the multiselect option (usually by long-pressing one of the emails first), then tapping on all of the emails you want to delete.
If you're using the stock Email app, the best way to make sure your email is synced everywhere is to use the IMAP server of your email provider (if available), not the POP3 server. Read about the difference here: IMAP vs POP3