How to remove sugar from juice
A blueberry contains ~85% water, 5% glucose, and 5% fructose (and it is generally considered a low glycemic index food, see e.g. this site). The solubility of fructose in water is extremely high (wikipedia says ~4000 g/L (25 °C), pubchem says "freely soluble in water"), and that of glucose is pretty high too, so there is essentially zero chance of removing these sugars through crystallization or other method without significantly altering the fruit or its juice. 

If you are still interested in generating an extract of the fruit, this article might be useful. It suggests two different approaches, juicing and drying. The first will generate juice and a press cake, and since the sugars are highly water-soluble the cake should be the reduced-sugar component of interest to you. You could also freeze dry the juice, assuming this contains the important components, then partially rehydrate the dry product and attempt to crystalize out sugars. Or you could dry the whole fruit and then attempt a separation with ethanol, with sugar extracted into the alcohol to obtain a reduced-sugar extract which can then be dried. Further separations with more apolar solvents might extract hydrophobic "phytonutrients" from the juice. But you are likely to remain somewhat in the dark with respect to what you've removed from the berry without further analytical tools to help you characterize the products.

There are alternatives to extraction of the sugar that involve biochemical conversion of the monosaccharides. One alternative is to treat crushed blueberry with xylose isomerase, which would convert the glucose to fructose. Fructose has a low GI ranking, which might be a benefit. Another alternative is to treat the blueberry with a mixture of enzymes (perhaps including sucrose-sucrose 1-fructosyltransferase (1-SST), see e.g. this example) that converts the glucose/fructose mixture into largely indigestible polysaccharides (soluble dietary fiber).

Otherwise the best solution might remain to eat the fruit raw or to seek other foods with similar composition and without sugar (perhaps you should consult a dietitian).