To delete a contact:
Sign in to Skype.
Find the person in your contact list. Go to the sidebar and click Contacts, then to the right, click Skype. (You may have to click >> to see all your contact groups).
Click the contact you would like to delete.
In the main menu, select Contacts > Delete Contact... Alternatively, press the Backspace or Delete key on your keyboard.
A message box opens with the prompt Are you sure you want to remove [name of contact] from your contact list? Click Remove.
The contact is deleted from your contact list. This means they cannot see if you are online, but they can still leave you offline instant messages.
You can block a contact to prevent them from communicating with you.
To block a contact and report abuse:
Go to the Contacts or Recent tab, right-click the contact’s name and select Block This Person...
In the message box, tick Report abuse if you wish to alert Skype of a nuisance contact.
Hope this helps.