For example, if a wizard were to dissolve some sugar in a bowl of water, or absorb some water into a sponge, or make some cake batter, could that wizard then Summon ONLY the sugar from the solution, the water from the sponge, or any specific ingredient from the cake batter but leave behind the water/sponge/batter?
I don't think Accio charm can be used to change chemical composition of different substances e.g. a solution of sugar and water.
My reasons are following:
In Half blood Prince's chapter "Birthday surprises", we come across the following activity of antidote making when Slughorn says:
"... which means, of course, that assuming we have achieved correct identification of the potion's ingredients by Scarpin's Revelaspell, our primary aim is not the relatively simple one of selecting antidotes to those ingredients in and of themselves, but to find that added component which will, by an almost alchemical process, transform these disparate elements--"
If Accio spell could work that way, instead of distilling different elements from the concoction, students would have just said "Accio [ingredient name]", measure their quantities right away to form an antidote. Of course always assuming that they would already know the ingredients using revealing charm. (Though vague commands did work too, like Harry saying "Accio Horcrux" instead of "Accio Slytherin's locket").
When hermione's Polyjuice potion went wrong in Chamber of Secrets, she could have just pointed her wand at herself and said "Accio Polyjuice poition" and wham, Poly juice potion would have been removed from her blood and system
When Arthur Weasley got attacked by Nagini in Order of the Phoenix, Healers at St. Mungo's could just use accio charm to extract the poison from his body immediately.
Every instance of the Summoning Charm is used on a discrete and tangible item - broom(s), books, brain etc. While the instructions might be somewhat vague ("Accio Firebolt" knows enough during Goblet of Fire to realise that it needs to bring the caster's Firebolt, while theoretically Harry could have used it in an instance where he was summoning someone else's with the same words, his intent was clear enough).
Separating a solution is an entirely different concept. You're not only talking about something that a person cannot easily visualise, the reality of how it would work is that you would need to remove every particle of a substance from another substance. That renders it fundamentally different from removing a visible brain from a tank of water. Even if you could convey the intent, it's unlikely that you could ever do it perfectly unless you were dealing with two substances that are already discretely separate, and maybe not even then (chemistry and physics being what it is).
Consider this too - do you expect the brain that Ron summoned was completely dry? Or that by summoning his broom, Harry coincidentally removed all the dust, stains, etc. that might have been on it in its original location at the same time? There's no evidence to suggest that is how the spell works, and it would need to work that way to have the effect you're asking about.