I am Canadian citizen with an Austrian passport as well. I wish to leave Pearson Airport using only my Austrian passport to live in EU. (I am in Canada a Canadian) Would this be acceptable?
The government of Canada won't check your passport upon departure, so this is not a problem.
Your airline will check your passport, but they just want you to hold a valid passport; they won't care what country it's from.
You will, of course, want to have your Canadian passport with you for your return to Canada.
I have dual citizenship in the U.S. & Canada, and I live in the U.S. Since I have relatives on both sides of the border, I have flown and driven across the border more times than I can count, presenting my U.S. passport when entering the United States and my Canadian passport when I have entered Canada. I have never once run into a problem with this. Since Canada does not have exit controls, I doubt that replacing "US" with "Austria" above will yield any problems.
Entering Canada, I always present my Canadian passport. This means that there's usually a part of the conversation with the border guard that goes like this:
Canadian border guard: Where do you live?
CBG: What's your legal status in the US?
Me: I'm a dual citizen. Do you need to see my U.S. Passport?
This is the sum total of the explanations I've ever had to give about having multiple citizenships and passports. (But then, I'm a upper-middle-class white male; YMMV if you're from a group that gets treated with more suspicion.)