Additional information is always good! It was hard to guess about plausibility without a motion of scale. As NeonKnight pointed out, it's certainly possible to get what you're asking about.
I would add that information on the intended width of the canyon would be good. Something like a slot canyon the better part of a mile deep is very hard to do. Something like the grand canyon, zion canyon, or yosemite is much easier to do. However, getting that much erosion over that much distance straight down from mountain peaks might be difficult without l larger area up to to deliver a concentrated stream of water.