On the page of the person you wish to remove, look just below their photo and biographical information and click the More... button. It will populate a drop-down menu.
In this drop down menu, select the second to last option called Remove Connection.
When you use this removal method, LinkedIn may let that user know you visited their page. After that, it only takes a few clicks to realize you've removed them from your network.
Also, when looking to remove someone, there's no confirmation box that asks if you really want to go through with the action.
As such, be sure you want to remove the person before actually clicking Remove Connection, otherwise, you may be stuck having to endure a little embarrassment
To start, look to the top of your profile page and click My Network.
Once at your My Network page, look to the left for the Connections option under Manage my network. This will bring you to the entire list of connections you've made while on LinkedIn.
Now, find the person you want to disconnect with by using the search function. You can search for the right contact by using their name, employer
Confirm your decision by clicking Remove. The person in question will not be notified by LinkedIn.