When I run r.resample to crop a map by using a vector and a mask, the resulting map has the same shape as the vector that I used but does not replicate (exactly) the portion of the raster map that I used as input in the r.resample. It produced a map with altered elevation values that is different from the raster map I used as input. I read that r.resample just "crops" the raster that is its input and does not alter it. I do not know why r.resample alters the output map
You can change the region resolution with
g.region rast=inputmap so the region will have the same resolution as inputmap. Then r.resample will output a map with that resolution. If that does not work you can try
r.mapcalc outputmap=inputmap instead of r.resample.
After that copy the colortable from one map to another:
r.colors map=croppedmap rast=originalmap.