by using a firewall you can have your computer ignore all those packets he sends. if your computer doesn't react to them they cause no trouble to you and won't overload your connection.
you simply have to configure your firewall right.

also, that person is not an 'mIRC member'. it's simply another user on IRC, who doesn't even have to use mIRC as their program to connect to an IRC network.

please note that mIRC is simply a chat program that connects you to an IRC network which provides the actual chatting service.
there are many more programs that are able to connect to IRC networks beside mIRC. mIRC is just simply the most known Windows client.