• Right-click or press and hold on to the contact you wish to block in Skype and select View profile from the Chats or Contacts tab.
• Block contact can be found at the bottom of their profile window.
• Note: On a desktop, you can also click Edit, then Block Contact from the drop-down menu.
  You can do the following from the Block this contact?. Abuse should be reported, and then the contact should be blocked: Turn the Report abuse from this person option on, choose a reason, and then select Block.

• If you don't want to report abuse, you can block someone. Block is the option to choose.
  • To confirm, select Block once more.
  • They will be removed from your contact list once they have been blocked.
  
  

Even if you ban someone in one of your groups, their messages will still appear in that group. To cease receiving their messages, you must remove the participant from that group. If it's a moderated group, though, you might not be able to remove them.