If it's like a Hickman line, then the larger cuff is there to hold it in place under the skin. To remove it, you'll get a local anaesthetic to numb the site and the person removing it will make a small incision and pull it out.
I currently have a Hickman line, and I have to say, I'm not looking forward to it being taken out. The whole idea makes me cringe (though I was fine when they put it in!).