Sure, but virtually all vegetables also have sugar, and I doubt the OP is eating a diet completely devoid of fruits, nuts, and veggies.
I eat a lot of veggies and some nuts. Vegetables and fruit have a lot of starch in them, which slows down the rate your body absorbs the sugar. I rarely eat fruit, most things are too sweet and disgusting.
You must mean simple sugar, right? Or do you really eat no saccharides?