Wrong song matched - Can I unmatch a song?

Delete the song from iTunes Match then in iTunes, change the name of the Artist (example, change The Beatles to "The Beatle"), run Match again and then the song should be uploaded (rather than incorrectly matched). After it's uploaded you can go back into iTunes and change the tag back to the correct artist and match will pick up this change too. Note that you don't update Match again after changing the artist name back; just leave iTunes open for a while and it will update this change to iTunes Match automatically. Note that it may take some time for this correction to show up on your other devices though.

Does changing a tag actually get a song to change status like that? Everything I've seen makes it look like it only looks at the waveform and doesn't use tags at all.

I'm not sure but I suspect it uses the Genius algorithm to match songs, which may or may not incorporate tag information. Since the tag is th only thing you can change it's worth a try to see if changing a tag will alter the match results. In my case all mismatched songs were the correct song and artist, but matched to the wrong album. The version of the song I had was very different than the matched song selected (mine was a live practice session version and it was matched to the final studio version) so the waveform would have been very different. That's why I'm guessing that it can't be using the waveform to match.

I've actually done tests where I've uploaded songs to iCloud with no tags at all, and they still match with the correct song. So if tags are being used, it's probably a very small factor in the matching process, and may not even be a factor at all.

This actually makes a lot of sense, as Apple is probably trying to avoid potential piracy - i.e. someone taking a certain song and tagging it as a different song, just to get a match. As to the OP's question, I don't know if there's a fix yet - I've actually called Apple support and suggested that a "force upload" option be considered, for a future release.