I think the answer is reverse osmosis. 1st reverse osmosis the salt because it is smaller than sugar. Then, reverse osmosis a larger size, for the sugar. So the order matters.
In osmosis both salt and Sugar are filtered. If you did only one component filtered (salt or Sugar), then I think osmosis is not a good choice. In osmosis only water molecules can pass.
Saeed Ayaz Khan why you say only water molecules can pass? It depends on the size. You 1st reverse osmosis the smaller stuff 1st, then, increase the size of reverse osmosis, to remove the sugar 2nd. If you remove the (bigger) stuff 1st, you remove it with the smaller stuff. So if the salt and sugar crystals are the same size, you stir it so the salt dissolves into water making it smaller than sugar.
Saeed Ayaz Khan because salt molecules can be broken into smaller Na+ and Cl- ions, which sugar cannot. As for how small can this be done at home, I'm asking this in a lab forum.
I think the best way for separation of two components is extraction if we ppt on component and filter. And then filtrate will be evaporated for next component separation.