It is not really common but it is used.  The ¨diminishing returns¨ is an expression I have heard often.

One thing that works to see different ways a word is used, and how common it is, is to use the word in youtube.com as a search term.  If you search for ¨diminish¨ at youtube.com, you can see about 640,000 hits.  You can see the videos that ¨diminish¨ is used in the title, to give you ideas of how people really use the word.  You can search for similar terms, such as ¨reducing¨  and ¨turning down¨ and you can see that those terms are much more commonly used.  

If you do this you will see that ¨diminished scales¨ seems to be fairly common in playing the guitar.  I have also seen the use of diminish used related to putting people down, such as in some of the videos there. 

I have found searching YouTube actually works better than searching Google when you just want examples of the ways words are used and do not want the definition.  

Instead of "diminishing the sound of the radio," most people say "turn down the radio." 

Instead of "diminishing the speed," most people say "slow down."

:)