CALGARY—In the escalating war of attrition among top oil-producing nations, Canada’s biggest oil-sands mines have a message for the market: Don’t look to us to cut production.

Long the unloved stepchild of so-called unconventional crude production, the oil sands have lured some of the world’s top energy producers to a remote corner of Northern Alberta where the heavy oil deposits are richest. There, they have plowed billions of dollars into building up a sprawling industrial complex amid the surrounding forests.

...