Cannas don't normally regrow from cut stalks like bananas do. The rhizome can put up a lot of new shoots if they're happy, but each time you cut them back it takes a little more out of them. You can certainly lift the entire rhizome out of the ground and move it to a new location, or even pot it up. Cannas store well when dormant, too.
Unfortunately, Stuttgart, like many variegated plants, is prone to burning and browning in the white portions of the leaves. Too much water, to little water, or too much wind, sun, or heat can all contribute to this. I grow it in full shade, where it gets a bit tall, but is more likely to look nice.
