On the assumption of the given meanings of the phrases, the whole sentence could be revealed as the following:
"My mother never gives anyone a hint because of demonstration of a principle."
It means "My Mother has a principle. This principle is that she does not give anyone a hint on smth." I do not know the whole context, therefore, I can't tell you the thing on which she doesn't give a hint.
Rover, does the phrase "give a tip" means "to tip smb" in most cases?
Isn't it used to say "give a hint"? it's interesting because I thought that native speakers say "to tip" instead of "to give a tip"..
The first interpretation to come to this native speaker's mind is that tip = gratuity.
The concept that someone might have a principled objection to giving advice, hints, that kind of tip is bizarre, so that simply would not occur to me.
On the other hand, many people claim that to have principled objections to tipping people.
The placing of on principle in the original sentence, of course, leads to the potential misreading.
<original> My mother never gives anyone a tip on principle.
<with a comma> My mother never gives anyone a tip, on principle.
<re-ordered> On principle, my mother never gives anyone a tip.