That's a tricky question to answer, Joe. It depends on what type of sugar(s) you are sensitive to. Joemama is mostly correct about beer having little residual "sugar". Most beer contains a few grams of residual carbohydrates in the form of unfermentables, but don't be mistaken; starch may be unfermentable, but humans can handle it with no problem.
The tricky part of your question, is that you can't have beer without sugar. So it's impossible to make beer without sugar. But good news for you (as I mentioned above) there is little remaining sugar in the finished beer.
I would recommend that you make only "small" low alcohol beers though. They will have less residual sugar than other "big" beers with lots of alcohol.