The humour comes from highlighting the disconnect between the self-proclaimed liberalism on the surface and the actual racism implied by the language used, a disconnect which is probably more common in white middle class society than a lot of people would like to admit. Hence it functions as satire.
Her intention in using a racist term was clearly to elicit a 'oh my god, did she say that?' reaction i.e. to be supposedly shocking. As you can see, along with her looking oh so pleased with herself for her 'wit':
She's an idiot. Who the fuck is she to tell Asian Americans whether or not they are offended by her use of racial slurs?
http://www.manaa.org/politicallyincorrect.html this is interesting.
Silverman "You're gonna teach me how to do satire?"
Well actually yes, seeing as you don't have the first idea how to be funny!
at 7:30, quite frankly the other woman would have been within her rights to have punched Silverman for being such a smug, odious dick. The host is awful too - two white people telling non-white people what they should be feeling. Glad the audience isn't as stupid.
Silverman - "We wouldn't have this forum (to talk about race) if I hadn't told that joke". What a fucking arrogant piece of shit.
On the other hand, Aoki comes across brilliantly, refusing to let the (white) host or Silverman lecture him as to how bad racism is or isn't, which they repeatedly try to do.
10:23 - one of the most gobsmacking things I have ever seen on TV. They bring on ANOTHER white person to tell non-white people that 'ironic' use of racist slurs is no big deal and....trust me, you just have to watch it.