Tyrannosaurs used their mouths to manipulate their food

Everyone knows Tyrannosaurs, especially Tyrannosaurus Rex, had tiny arms compared to the size of their bodies. Although counter-intuitive for humans who do almost all their manipulation with their hands, the Tyrannosaurs could use their mouths as an all-purpose tool for feeding.

T. rex cast, showing it's massive jaws and puny arms (Wikipedia)

Not only could they bite of chunks of meat with their powerful jaws, there is fossil evidence that shows that they used their mouths to turn over the their food to get at the rest of the meat.

From the remains of a hadrosaur that was partly eaten by a Tarbosaur (a close relative of T-rex) it is clear that the Tyrannosaur extensively manipulated the carcass with their teeth. 

Tyrannosaurs did not just rip apart carcasses and crunch through bones even though they could. Sure on some occasions they did, but not always. They could, and did, chose how to feed and could be relatively delicate.

Dave Hone, Selective feeding by Tyrannosaurs 

 In this case the Tyrannosaur most likely tore the bone from the rest of the carcass and scraped the meat off, using the front teeth in it's upper jaw. The U-shape of the upper jaw meant that Tyrannosaurs had a relatively straight row of teeth at the front, perfect for scraping meat of bones.

With smaller prey Tyrannosaurs weren't this precise, a Tyrannosaurus coprolite found in Canada was filled with the crushed bones of a young Dinosaur. The Tyrannosaurus had simply gobbled it's prey, crushing and swallowed the bones along with the rest of the animal.

The paper on selective feeding by Hone and Watabe is available online: New information on scavenging and selective feeding behaviour of tyrannosaurs