To grind or crush something with the teeth. The dog managed to chew up the entire shoe before anyone noticed.
To damage or destroy something by chewing. The paper shredder can chew up a stack of documents in seconds.
To consume or use up resources or time. The project is starting to chew up more time than we initially planned.
To criticize or reprimand someone harshly. The manager chewed up the team for missing the deadline.