I’ve heard this phrase many times, and I have no idea what it means.
You say it when revolted.
It means (or meant, back in the Dawn of Time known as the 1980’s when it was used unironically) “I find that course of action/thought repugnant and would not willingly choose it.”
As in:
“Like, did you hear bellbottons are predicted to make a comback in the 90’s?”
“OH! That’s, like, totally gross! Like, gag me with a spoon! I have no idea what they’re thinking. Now, like, hand me that Aquanet and a hairpick.”
The phrase was also used as part of an error message in the fictional esoteric computer language VALGOL
I first heard it in Moon Unit Zappa’s Valley Girl c.1980/81.
As others have said, the phrase was used when you find something revolting. You know how much better you feel after you vomit and get rid of whatever it was that was making you nauseated? I think it’s like that. It’s like when you open your mouth wide and pantomime jabbing your finger down your throat to indicate revulsion. Why a spoon? Well, it fits the song’s rhythm better than ‘Gag my by putting your finger down the throat!’
Fac me vomere per cochlea!
Which sounds like it has the potential for being a bilingual pun… 
Well, a spoon was (is?) also a recommended method to induce vomiting in case you ingested poison.
Because it’s dull, it’ll hurt more!
or…
there is no spoon
make your choice 
Well, you are talking about San Fernando Valley Girls. Since the silver spoon is already present, may as well gag 'em with it.
Okay, fine.
Fer sure, fer sure.
She’s a Valley Girl
and there is no cure.
Incidently, Valley Girl is only a Moon Unit Zappa song in the sense that she sung the VG parts. It was written and composed by her daddy, Frank, of course. IIRC, Steve Vai played guitar on it too.</useless trivia>
I have also heard this version:
“Gag me with a briefcase”
Which I think is even more effective than some ordinary spoon.
Actually, the word ‘sung’ is used very loosely here. :smack:
That’s too funny. 
The one I always heard and used growing up is “Gag me with a shovel.”
Heheh. Alternatively, I’ve heard “Gag me with a pitchfork.”
Yum.
Once, my friends and I put together a ‘punk band’. (Lasted one afternoon.) One of the lyrics I contributed was ‘An impromptu vivisection with a dull spoon’.
A parody of that expression I heard during the Valley Girl days was: “Gash me with a Ginsu!”
It means you’re too freakin young.
We bastardized it to be “gag me with a king salmon”. And they were Matsu Valley girls, rather than SanFern
True, although I would suspect that the origins of this phrase have more to do with bulimia than concern about injesting poison.
Questions like these make me feel old.
(Because I SO totally knew the answer.)