You can control which members you want to remove from your connections in your Dashboard.
Go to the Dashboard, then click on 'Your Connections' > 'Connections'. Beside the name of the member you no longer want to be connected with, click on the button 'Remove User'.
This action cannot be undone and members can only reconnect with you if they send you another new connection request.
You can add the connection again, so say if a user removes a connection both you and the person you were connected with can still add each other again.