Better check if there's anything to cut at all beforehand. Generally speaking this is a very valid tip - but don't cut before you have checked with an analyzer+ears if it's needed at all.
When i listened to the first version i thought it was way to much verb. clear the mix BEFORE whacking reverb etc. etc. over the mix. It's the icing on the cake, not the foundation.
A/B with released tracks is a very good idea as well as has been said before.