Yeah, if you have a Dremel + cut-off wheel, use that but if not, spend the money to get a proper cable/housing cutter. Park's is excellent but the Performance one works just fine, too.
I use the old cable to open up the plastic inner sleve after cutting. Run it through then kind of angle it out to the side while pulling and rotating...kind of hard to describe I guess but works well. Or use an awl or heavy-duty paperclip in a pinch.