I have no experience with Twitch IRC servers, but I looked at the code of a friend of mine who does and I see - according to https://github.com/craze/TMI4mIRC/blob/db9fd4b92847d4aa6afd4f7232c51ed14fe0c68e/tmi4mirc.mrc#L338 - that to ban someone you use:

Code
.privmsg $chan .ban $1


...where $1 is the nickname of the person to ban...

Also, I know SReject made a set of twitch scripts for mIRC and looking at https://github.com/SReject/mTwitch/blob/master/README.md I read that there's a #mirchelp channel where you might be able to ask for more information about mIRC + Twitch.

Hope this helps somewhat!

GNU Terry Pratchett - Looking for a mIRC help channel -> Check #mircscripting @ irc.swiftirc.net