I have an iPad rather than an iPhone but the settings should be the same. On my iPad, I have the setting to "sync all unplayed". After a specific podcast episode is played fully, on the next sync, it is removed from the iPad, but stays on my computer. Partially played podcasts are left on the iPad. This is true for both video as well as audio-only podcasts.
Rereading your post, are you wanting to delete the podcast from the computer, but leave it on the iPhone? That might be possible, but I'm fully certain. Me personally, I treat the computer as the "master library" and podcasts I want to keep are on the computer, rather than just my iPad. That way if I break or lose the iPad, I still have the podcasts and can sync them back to my replacement device.