Understanding the Canadian Phrase: I'm Done My Beer

I have a bizarre completely un CX related question. If I said the phrase " I'm done my beer" does this phrase make sense to you? I just saw a video, where someone said this is a very Canadian phrase. And in most of the world, including much of the USA, this phrase does not make sense without the word "with" added. In Canadian English, if I added the word "with" to that sentence, it actually changes the meaning of the sentence. Of all the Canadian-isms that I have heard in my life, this is completely new to me...