You can do it with normal removal to clear Mizzix and his artifact ramp. Some stax effects might help too to slow it. Tax effects (like Thalia), cards time shit down artifacts like Stony Silence and Collector Ouphe, and cards that prevent casting like Gaddock Teague and Rule of Law.
At the end of the day, a combo deck isn't particularly strong in 1v1. You just need to run some cards to deal with it. If you don't, of course it's going to annihilate you every time.
I hope this post doesn't come off as hostile. Just trying to help! Banning your friend's deck seems like an extreme measure so I'd like to help you avoid that necessity.
You aren't coming off as hostile at all!
I've played against the deck with my Atraxa, Karametra, Mina and Denn decks (which are all my most dialed in decks), as well as a few other ones I've tossed together. I already have the reputation of making decks that aren't fun to play against (Atraxa has a bad rap just because I run a semi-reliable land base, Karametra has some soft stax effects, but nothing too oppressive, and Mina is essentially a Valakut deck with some land destruction), which is why I've avoided going full Stax. I don't want to build a deck just to try to slow down Mizzix. It's easier for him and I to just play one vs. one games with other decks.
Again, if I'm actually playing a multiplayer game and he uses Mizzix I wouldn't care at all.
I would also argue that combo decks in a one vs. one setting tend to perform better than in multiplayer. Dealing with only one players worth of counters or other interaction is way easier.