The noble idea in iOS 8 and OS X Yosemite of making your Apple devices work together better turns continuity into annoyance.
Apple’s new call forwarding feature might not be so user friendly. Answering messages and answering calls on whatever Apple device is convenient (your iPhone, iPad, or Mac) can be a headache. For instance if a call comes in, it will ring to the iPhone first, then a few seconds later to the iPad and Mac. Due to this delay, answering the call on your iPhone doesn’t stop the other devices from ringing. And you can be left with multiple devices all ringing at once, creating a cacophony of sounds.
An easy solution, turn off notifications.
Go to System -> Preferences -> Notification -> Messages adjust the Messages alert style to None. You can also turn off sounds from this same location, uncheck Play sound for Notification.
If you prefer to receive messages only to your iPhone you can turn off iMessages to your other devices.
To stop forwarding to iPad or turn the notification sound off
Settings -> Messages, switch off iMessage
Settings -> Notifications -> Messages -> Notification Sound -> None
Stopping iMessage on your Mac will disable all features, including send, receive, and read.
Messages -> Preferences -> Accounts -> Apple ID, uncheck Enable this Account