How do I stop my Mac from attempting Time Machine Backups?
If you're referring to the nag when you plug in a new disk, you can try the defaults setting mentioned here:

defaults write /Library/Preferences/com.apple.TimeMachine DoNotOfferNewDisksForBackup -bool YES


Alternatively, try decreasing the interval of backups to some insanely great number. Try the opposite of the setting listed as #26 on this page:

defaults write /System/Library/LaunchDaemons/com.apple.backupd-auto StartInterval -int 1800


You might try this to have TM prompt you once anually:

defaults write /System/Library/LaunchDaemons/com.apple.backupd-auto StartInterval -int 31449600


You might need to use sudo to apply these settings.