Aspergillus oryzae (koji)
Look up Aspergillus oryzae. It is a member of a very abundant group of molds Aspergillus and this microorganism actually creates simple sugars from complex carbohydrates. So I think it works well with what you are looking for. It is not a bacteria, but I guess the gene clusters could be transferred from these fungal organisms to bacteria, if needed. As far as "non carbon based" goes, however, I think it is not compatible with the very nature of what sugars are! (basically carbon chains).
I don't know if they "discard" the sugars, per se, but they clearly don't use them. Indeed, in the process of making saké, there are two "fermentation steps". The first "fermentation" is done with koji, which is a starter culture of Aspergillus oryzae. I use quotations for "fermentation" as it is in fact a saccharification process. And the koji molds don't use the fermentable sugars, because the actual fermentation is done in a separate step (meaning the sugars have accumulated in the culture medium, before the actual fermentation).
The actual fermentation is done, of course, with a strain of the classical wine yeast saccharomyces that use those sugars and converts them to alcohol. Yeast can not use complex sugars to produce alcohol, which means that Aspergillus oryzae produce true simple sugars.
Considering that saké are usually very high in alcohol (commonly 12-15% abv) and that fermentation is not sustainable above 15% abv (for most yeast), it means that they have access to large amounts of fermentable sugars generated during the koji "fermentation".
So these Aspergillus guys use complex carbohydrates as source of food (like starch of cellulose) and output simple sugars. They are also used for the preparation of certain foods.