It took me a bit of searching on youtube and the internet for a recent layout of linked in an how to remove a contact.  As of 3/28/2014, this is where I found the option:

1. go to http://www.linkedin.com (sign in)
2. at the top row go to: network > contacts
3. at the page with a listing of all contacts, the easiest way is to hover over a contact where ‘tag message more’ options show up > select more > Remove connection

From the forums I have read, the user you remove gets a message that you have removed them.  I haven’t tested it out but I am assuming you wouldn’t care if you don’t know them 🙂