You can only delete all the messages to one user by control-mouse click and select "Delete conversation." Similiar the Edit menu on the iPhone will let you do that on the iphone. Individual messages can't be removed on either. There are applications on the App Store that let you extract messages from iMessage on the iPhone backup and save them to your computer as text files. Once done, you should back up any important conversations to an external hard drive or the cloud as a data file separate from iMessage, and then you can clear a conversation from your phone or computer.