If there is a user you would no longer like to connect with you can block them. Do this by long pressing on your friend's name and tapping "Block".
You can also block a user by swiping left on their thread. Tap More then select Block.
By doing so, you will no longer see any of the messages that user may send. Keep in mind, this will not delete any messages you have already sent this user. So if you want to also delete any messages you have sent them- take that step first to delete all your sent messages to them, then block them.
Please note that if you send this blocked user a message after you have blocked them- they will be unblocked.