You will most definitely have to reinforce the bodyshell if you cut the roof off-Mini's a unibody, like most modern cars, so cutting the roof off will make it practically fold up in the middle. I've seen many "convertible" Minis in various British car magazines, many of which were converted using kits of some sort to help smooth out the bodywork at the back of the car. They also, I figure, would include ragtops complete with frame and fabric. Also, every single one of these converted Minis I've seen has a rollbar of some sort, usually tied in to the windscreen like a Triumph Stag, T-top style. Seems like the easiest way to reinforce the bodyshell. If you can live with having the rollbar (think something like an early VW Cabrio), then go for it. Would recommend cruising over to the websites of any Mini specialists in England for some more info, too.
Hope this helps, sounds like an interesting project.
-William