As James K said, the most common usage is "ramification of something".
Can you say:
The negative ramifications from absent parents are obvious.
Yes you can. But it is more commonly expressed as "ramifications of", as others have already said.
You are correct in that you have spotted a somewhat tautologous use of "ramifications that result from". Is it illogical or wrong? Not quite, but sort of. Negative ramifications can literally result from another action, even though they are themselves (almost invariably) negative outcomes of another action. It's a kind of recursive sentence. But I very much doubt the author of the sentence thought of any of that. I think they just picked a clumsy preposition.
If, for some reason, I really wanted to say "from" rather than "of" (and I can't think of a reason why you would), I personally would word it like this:
The negative ramifications arising from absentee parents are obvious.