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I am Vinod. I will try my best to help you resolve this issue.
What I understand is you want to turn off the message facility on the mac, correct?
For that you need to turn off imessage from the Mac as well. On your mac, please go to Messages app, click on "messages"at the menu bar, click on Preferences and then on Accounts.
There, select iMessage in the left column and click on sign out.
Hope this helps. Let me know if you find any difficulty.