It isn't recommended. Cutting open the base opens the plant up to disease. Roses typically aren't propagated by root division. If the variety isn't under patent, you can take cuttings and attempt to root.

I know almost nothing about doing this, except to say that there are types of roses (when grown on their own roots) that sucker freely. I've heard of folks having to contain the spread of these types (the "gallica" class of old garden roses for example) by digging them and then dividing.

I would imagine that your rose isn't one of these, however, and even if it were it's probably not of a size yet to respond well to having a section of it hacked off. If your purpose in doing this is to make more plants I second Diane's advice to just make some cuttings and root them. There are several threads on this board about how to do this...I haven't tried it yet on my own roses, but it looks pretty easy (and fun).

Claire