"Spaz" does not resonate the same way in the US as it does in the UK; it is more like using the word "idiot." There are a lot of reasons for this, one of which is that "spastic" was never generally used in the US for cerebral palsy as it was in the UK. With more globalized discussion, however, it is becoming less acceptable in the US.
^This.
Growing up in the US, I didn't even learn the origins of spaz until I was well into adulthood. Now I just sort of shy away from it. It's not offensive, but it's not used as much as it used to be either. It's meaning of idiot has been replaced with derpy or derp anyway. Cartoons have cut it out completely in the last 10 years.
But the US had no problem slinging insulting words such as gay, retard, mental quite flippantly. In the 90's the most popular phrase here was "Oh. My. Gawd. You are sooo retarded", now you'd turn heads and get dirty looks. It hasn't been until the last 10 years that those terms were seen as damaging in the first place.
It was never PC, it just wasn't seen as utterly offensive as it is today. Tropic Thunder's "Full retard" quote never would have made it to cinemas if it was made today. Which is a good thing. But lots of offensive words don't really resonate the same way in the US because "shock humor" and one line "zings" where characters insult each other is very popular and still uses sexist/racist/disabilist insults to get laughs. I have a theory that since we're a more physically violent culture we put more stock in our actions instead of our words than the UK, so they don't carry the same weight when you throw an insult, if that makes sense.