I have watched this movie 15 years ago and I can't recall the name of this movie.
The movie begins with a scene where a women driving a mining truck in a snowy work place, the women got a retarted son ( I think he got in a car accident ) and he can't remember events.

She is a single mother.

After a long period and her son hits puberty, she got a call that her son is in the police station for doing something bad, the mother comes to the police station and asked her son where is the thing, and he lies and says he can't remember, then she yelled at him and she says : don't lie and you can remember.

That's all what I can recall from the movie.

Are they Asian?
It could be a movie called "Mother"
A Korean Film which seems to be much of what you describe.

Mother (2009) - IMDb (http://www.imdb.com/title/tt1216496/)

Many thanks akf_ngu, but I saw the movie 15 years ago, so it might be filmed at 90's
Another thing, the boy got caught for a minor thing, not murder.
I'm sure it's an american movie.

Ahh well then I am at a loss sorry! This is the only movie I could find that I thought might be it.