What options does a mod have at Twitch?
That varies a lot, whether the streamer still has a streambot that offers further possibilities, but here are the basics;
You can give people a timeout for a period, during this period this user can no longer write anything in stream chat.
Furthermore, you can permanently exclude users from the stream chat with a ban.
You can change Auto-Mod settings in the stream, put words on the blacklist that may not be written in the chat, words on the whitelist.
Then you can activate the follower only chat, then only people who follow the streamer can also write in the chat, then there's also an emote only chat, so only emotes in the chat. Yeah these are so basic things that have come to my mind now.