"tearing chunks" is a correct and usable phrase in written English.
It is typically used to describe a forceful or violent action of tearing something apart or breaking it into pieces. Example: The children were tearing chunks of bread and throwing them to the ducks at the pond.
Five was happily tearing chunks from his baguette with his new front teeth.
We eat the salta by tearing chunks from the hubcap-sized, blistered, hot pita and dipping them in the stew.
This early on, Mr Miliband's task is easy to describe: to look plausibly prime ministerial and economically competent, while tearing chunks out of the government.
In so much as Labour and the Tories were discussed, it was mainly in the context of how they were being affected by the insurgent rivals that are snapping at their legs and tearing chunks out of their vote.
The Conservative party has been tearing chunks out of itself over Europe for decades and it's conducting the final stage of that battle while in government, to the detriment of us all.
Grown-up to-do list: move to area with good schools – check, start going to church – check, join gang that tortures animals – check, pay good money to watch two young working-class and/or black men tearing chunks out of each other – check.
Ike tore chunks off the stadium's retractable roof.
As the dogs tear chunks of flesh from the terrified pig, the hunters undoubtedly feel proud of their accomplishment.
On Monday night, Panorama and Newsnight went head to head in a battle to tear chunks out of their bosses.
Remove from oven, trim off any charred tips, and tear chunks into irregular pieces, from 2-inch wads to large crumbs.
It won an impressively large number of seats, partly by coming through the middle as the Liberal Democrats tore chunks out of Labour.
