No. The overall canyon system of the Barranca del Cobre or Copper Canyon (27°30'58''N 107°45'57''W) is larger and some portions are deeper, than the Grand Canyon in the United States.
The answer to this question depends on how you want to measure it. Here are several answers from the Grand Canyon National Park web site:
(http://www.grand.canyon.national-park.com/size.htm)
The...