Hmm... I believe I've never gotten any nasty critique, lucky me, but there's been few... I'd say "insensitive" or more like thoughtless critiques left for me. As I saw them, they weren't nasty, just phrased little off, and so I had no problem whatsoever with those.
I'm not sure how I'd take really nasty, rude critique. I'm pretty tolerant but I bet I would be offended if someone did that. LOL first I'd probably just take a moment to calm down and swallow the worst anger.

And it really depends. If the critic goes bashing the theme/topic of the artwork (like if it's yaoi or fanart or something like that) just because they don't like it, presenting personal preference as critique, it's very unnecessary and I don't see any reason to tolerate that, I'd probably brush them off with some light comment and ignore them. (though if someone just says that they don't like some work of mine (and maybe why so), I don't get offended or angry)
If someone is obviously just being rude and nasty and won't drop it if asked I'd rather just block or report them.

And if the critique is given in a cold manner but for a reason (like anatomical mistake etc.). I don't necessarily like it but I can take it (and the person could just have more "analytic" standpoint).
Though I do respect a LOT more comments and critiques from people who are respectful from their end. That kind of critique I happily receive.
It's no wonder if artist gets pissed if someone is being rude and nasty. And if you ask me, it hardly makes one any less an artist if they don't take well critique which was written in a bad manner.

It tells a lot about the person if it's too hard or below them to give constructive advices to artist and instead act up and be insensitive. Not cool.

I took 'Accept the critique, althought it has offended you.' because everyone should be able to accept critique. Even if I'd write him a note, that his/her chant wasn't very nice and I felt offended a bit by it.
Sad I had to learn that many people feel a triumph about such re-notes but I don't care really anyway.
Constructive critique is more my friend and more helpfull.

mmmmmmmm reply in a cold way cause i FUCKING HATE WHEN THEY DIO THAT!!!
ONE OF MY FAVORITES ARTIST IS GOING TO LEAVE DA JUST BECAUSE OF THAT GROUP OF MORONS D:<
AS ALWAYS,IF YOU DON´T FUCKING LIKE,WHY IN HELL ARE YOU FUCKING WACTHING IT
in others words,i´ll kick they´re asses =-=
and i´m already spyco in a normal mood,youDON´T wanna see me angry

I choosed that "reply" option, but it would really depends if that person only want to brake me down with nasty rude words or just wants to show me "cruel truth" but without rudeness. and if I would feel that he/she is not that much right..or he/she is only looking for mistakes. I would rather try to vindicate or defend but withou rude word. I don't want to argue(or even fight) with someone.

I'm really sensitive about drawing and other things and very instable in moods so I don't require critiques. But it's not like I think I'm perfect.. or don't want get better.. no it's not like this... but.. bad critique really discourage me in creating.

when you say ctitique when there just like everything is wrong all of it!! with a few sentance enhancer such as this is garbage or crap
or is it just a whole bunch of them pointing out flaws,?