Yahoo Mail – How to Stop Automatic Logout from Messenger

As I know, You need to delete them from "Contacts" tab in your Yahoo mail.

1. Check the box next to each contact that you want to delete.
2. The right side of the page lists several options.
3. Click the Delete option, and then confirm the deletion.

The names are moved to your Deleted Contacts where you can restore them if you like.

See How Do I delete a contact?.

It is possible to remove the binding to these services at any time.

Resolution
To disconnect your Google or Facebook account from Yahoo!:

1. Sign in to the Yahoo! Account Information Page
2. On the sign in form, click Sign in with Google or Sign in with Facebook
3. Enter your Google or Facebook login information
4. Click Manage Other Accounts to Sign-in
5. Click Remove next to the Google or Facebook icon. A pop-up dialog box will open prompting you to confirm the action
6. When finished, click Sign-out at the top of the page

From this Yahoo help page.

Deleting the Facebook contacts from Yahoo is the same as for any other contact.

Deleting Facebook contacts is the same as deleting any contact. There are no special measures that must be taken simply because the contact was imported from Facebook.

You can see the contacts of your most recent Facebook import by going to View and selecting View Last Import.

Note: If you have done multiple Facebook imports, you will only be able to see the results of your most recent Facebook contact imports.

From How to delete Facebook contacts.