For deleting SharePoint groups you can use SharePoint Designer. For this you should open site in SPDesigner, in left column goto "Site Groups", select groups for deleting and press Delete button on keyboard or in ribbon. But this process doesn't always work. And when I wanted to remove user groups SPDesigner hanged and reported error of deleting.

So I decided to use PowerShell for this. It's rather short but very heplful. Add to my instrumentary.

I selected user group names and added them to array $groups in cycle remove groups.