How do I unsync iMessage on my Mac?

You have a couple of ways to configure this. First off, make sure both the computer and iPhone have been set up to use the same Apple ID.

1. You can disable Messages.app's ability to receive text messages on your Mac:
   • Open the Messages application. Access your preferences by going to the menubar and clicking Messages -> Preferences...
   • Under the "Accounts" tab, you will see all the accounts you've set up to use with Messages, including iCloud. Selecting "iCloud" from the options on the left side of that screen will show the email addresses you specified and your phone number.
   • Unchecking these will disable the ability of Messages.app to receive those messages you wish to send only between mobile devices.
2. On your iPhone:
   • Tap "Settings", then scroll down to "Messages" and tap it.
   • Scroll down to "Send and Receive" and tap it. Look for the menu option heading that says "You can be reached by iMessage at:", which has your phone number (checked by default) and the email account you configured when you initially set up your iPhone. This is probably your apple ID, but can be any other email address you've specified.
   • Simply tap the email addresses that are checked to disable them. This should force messages to communicate with only your phone number.

It should work by disabling all but your phone number on iMessage, but you may need to disable everything on your Mac as well. A little experimentation and tweaking should get you set in just a couple of minutes.

Turn it off in the iCloud settings. System Preferences - iCloud