Is calling someone a stupid idiot redundant? I know there are “Idiot Savants” who have some very intellectual abilities so maybe a distinction needs to be made? It just seems unnecessary to me.
Unnecessary and hurtful 
It depends on the person you’re speaking to, I suppose. It could just be a pleonasm.
Wouldn’t that make it redundant? Would calling someone a “stupid, idiot savant” be a contradiction or are there people out there who count uno cards?
I think there is a subtle difference between “stupid” and “idiot.” I might call my slow but good hearted co-worker “stupid” but she isn’t an idiot. And conservative radio commentators sure are “idiots” but they aren’t necessarily “stupid”- they’d never make all that money if they were outright dumb.
So I think “stupid” can modify “idiot” in a meaningful way.
I have never heard the phrase “stupid idiot” used in a fashion that did not demean the speaker more than the spoken-of.
Putting aside whether it’s hurtful, it’s a clumsy locution that makes the speaker sound none too clever him- or herself.
I find “stupid fool” to be more satisfying
Both words have a range of meanings, and only in one combination are they at all redundant.
Stupid can mean: to be stupified, lacking in sensation, morally insensible, slow witted or slow in thought, inanimate, boring, stubborn.
Idiot can mean: a person without learning, someone permanently devoid of ordinary reasoning or rational conduct, someone you think is acting irrationally.
Possibly you can include “slow witted” in “devoid of ordinary reasoning,” but only at a bit of stretch. Other than that, you have a wide range of insults available.
A stubborn uneducated person perhaps? Stupified and incapable of reason? Morally insensible and acting irrationally? Almost unlimited fun to be had. 
I doubt anyone really believes that the speaker of “stupid idiot” is attempting to wield these words with the surgical precision some posters here are describing.
Redundancy/superfluousness of descriptives is a common ploy for adding emphasis, e.g. “this is really, really bad,” or “that was a stupid, stupid move.”
The “stupid” in “stupid idiot” is superfluous, but adds emphasis. It’s more polite than, but means no less than, “fuckin’ idiot.”
I agree.
If I call someone a ‘bloody idiot’, it doesn’t mean they have a wound!
Well, for one thing, “stupid idiot” rolls off the tongue easier than “idiotic stupe.”
The words don’t always convey the same thing, but there is some overlap in their meanings. There’s some overlap in their spelling, too, which can be exploited by calling someone a “stupidiot.”
Mainly, though, it’s just a way to add emphasis that doesn’t sound as redundant as “idiotic idiot.” 
Actually, “idiot” used to be a clinical term for an individual with the most profound level of mental retardation – a person with an IQ of 25 or less. “Imbecile” was used for people with IQs of 26-50, and “moron” referred to those with IQs of 51-70.
And now they ALL are used to refer to Rush Limbaugh.