I was reading this entry in hopes to figure out my husbands issue with trying to remove his brother from his Note 3. Nothing anyone said helped, and then it finally came to me and I feel so stupid. I have the Samsung S5 so it's set up differently and I do have the three dots that everyone is talking about. But for the likes of Note 3 and other similar devices...
1. Settings
2. Accounts
3. Google
4. Choose account and let it open to the sync to where you choose what syncs or not.
5. Hit the soft key on your phone that has the three lines. It should be at the bottom of your phone on the left side of your button. It will then pull up the 'delete account' menu option on the bottom left of the screen.
Hope this helps all those past who haven't figured it out yet and all those in the future who have the same issue.