Can iMessages be deleted permanently or at least kept either on a phone or a computer, but not both? I would like to stop messages on my Mac from loading up all the messages I have on my iPhone when I plug it in. 

Scenario: receive 10 iMessages on my iPhone during the day. I then delete them. So messages inbox on iPhone is empty. 

I then plug phone into MacBook Air at the end of the day. When I open messages on the Air, and all messages load up, even though the ones that were deleted on my iPhone.

How do I stop this from happening?

I would like my iPhone messages to stay on my iPhone only, and my computer messages to stay on my Mac only.
It sounds like you simply have iMessage enabled on your Mac (which doesn't have anything to do with plugging your phone in, since your messages are synced through iCloud).

Anyway, just open up Messages (iChat), go to Preferences > Accounts, select your iMessage account in the list on the left and then unchecked the "enable this account" checkbox.