Sign in to your skype account via skype.com, on your profile dashboard scroll down and find Settings and preferences section, and enter to Account Setting.
On the setting page you will see list of microsoft account is linked to your skype, just click on Unlink
then click to Continue when this question appear
if succeed you will see this message with the status Not Linked, thats mean your skype is successfully removed from your microsoft account
Now try login to your outlook/live account, as you can see there is no skype chat as well as the contact list anymore.
Next make sure the local record on your computer are gone also, we will discuss this on next post, don't let your privacy leaked XD