When I wrote my CV, I found that I would like to say "Honorable Mention at Mathematical Contest in Modeling", but I put on "Honorable Mentioned" instead. After searching on the internet I found no one use this pair of words. Now I am wondering if writting "Honorable Mentioned" is plausible?
Your best bet is to say "honorably mentioned", or looking to rephrase your sentence altogether to something more similar. It may not be used, but it is grammatically correct and still keeps the flow of the sentence going. Either way, you definitely want to put in your CV that you had an honorable mention in the past, but make sure that the flow of the sentence is good. Words with a -y suffix is not unusual for sentences like these, definitely wouldn't raise a hair with anyone reading it. You could check the dictionary definition to refer if you decide to rephrase the sentence;
"a distinction conferred (as in a contest or exhibition) on works or persons of exceptional merit but not deserving of top honors"