Hi,
I have been very curious about this. I visited Carnegie Mellon's official website and they state that they require one to send all scores for SAT I, SAT II, or ACT and that they give weight to the highest score. I scored a 32 on my second ACT (E: 35, M:30, R:31, S:33) and a 28 (E:29, M:32, R: 24, S: 28) on my first. As you can see, my composite score is higher for my second, but my math sub-score is higher in my first. I went on PrepScholars.com and they said that Carnegie Mellon does not superscore the ACT. However, the website also said that another school I am interested in did not superscore and when I went on a college tour for that school, they explicitly stated that they do in fact superscore the ACT. So can anyone give me a clear answer to this.
PS: I know that a 32, although a good score, does not place me favorably in admission.
Call the admissions office at CMU and ask.
They don’t say they superscore so don’t assume that they do. CMU as much as any school - and a lot more than most - knows a thing or two about score distributions. They want all the data because that would reveal more of a true indication of your abilities in this area than just one set of scores.
What they actually say is this: “While we’re interested in the general pattern of your scores, we give most weight to the highest score you’ve received on any of the exams”. Another way to say this: while they give the most weight to your highest score, they are taking the pattern into consideration. That’s where things can get very interesting, depending on how many times someone has taken the exam(s) and what that pattern of scores actually looks like. It’s easy to devise models that account for variability, direction of the trend, and so forth. And they’d need to account for scores from a “one and done” vs. scores from one, two or more retakes. My guess is that they look at all of that, and hopefully the timing of your tests as well (they prefer tests from junior and senior year).
In your case, you clearly showed significant improvement on the second test for three subjects and delivered a consistent result on the Math. So perhaps they will view your “true” math ability as somewhere in the 30-32 range and closer to 32 than 30 (or even 31). How they are going to view your remaining subscores is anyone’s guess, but hopefully they will assign a significant amount of weight to the stronger scores. While it’s very easy to tank a test (especially the first one) it’s much harder to accidentally ace it! So that’s potentially good news for you.
The previous paragraph is nothing more than an educated guess, btw. My D17 has taken 2 ACT’s (her smallest improvement was - of course! - math) as well as an SAT (where her math score is consistent with her best ACT) so I’ve been thinking a bit about this issue as well! 
Good luck to you!