How to filtrate sand from sugar the Dune way? 

Everyone on the internet: "The spice must flow." Cube Chemistry: "Actually, the spice must drip."

Neat! Haven’t seen dune 2 yet, but being that water is so rare on Arakkis that spitting on someone is a gesture of politeness for giving them your moisture, I don’t think separating with water would be a good way would it? My first thought is to use spinning chambers of various hole sizes to filter out the very fine dust spice from the heavy grains of sand. From there you can sift in a vibrating bed to separate light particles from heavy particles. There’s steps from there for further refinement but truthfully it doesn’t seem that finer refinement from that is necessary for how they use it

Wouldn't it also be possible to use a mechanical process instead? If you assume spice has buoyancy in moving sand

Hot water would provide a better if not near 100% yield. Water heating solar panels would cheaply provide the heat. The water shouldn't be too much of a problem since it could be easily condensed and recovered for reuse, and the cost of spice is more expensive. The heat from the sun to recrystallize would be cheap as well. Of course this all depends on the solubility of the spice (after looking online, it looks like water is hard to separate from spice). Different solvents could be cheaper/better.

"I think easily accessible cinnamon who does not dissolve in water resembles spice pretty good, so let me demonstrate with sugar instead" ;-) Even with little water, they could use some kind of reflux if the spice is water soluble.

carefully calculated cyclonic filters... denser material will fall out first.

Some spices are also water soluble. Can you reclaim those spices in the same way, or does this only work for sugar?