At this time/At this point, we can tell a boy and a man apart by what they do.
I want to express the situation like a disaster suddenly happened in a family.
Is my sentence right or wrong, can you understand it?
I think your sentence is fine, but you might consider changing your opening clause:
In times like these, we can tell a boy and a man apart by what they do.
This expression is often used to refer to a current episode of trials or troubles.
There is nothing wrong with “At this time” or “At this point”, but neither of those implies a time of hardship the way “In times like these” does.
In part, what you're trying to say seems a bit odd because it's so close to an existing idiom in English. It almost sounds as if you were trying to use separate the men from the boys or sort out the men from the boys but failed.
This is what separates the men from the boys.
It's understandable, but it's not completely clear. You wrote,
"...,at this time/at this point, we can tell a boy and a man apart by what they do."
I would rewrite it to say,
"...,at this time/at this point, we can tell a boy and a man apart based upon what each one does."
That doesn't mean yours is wrong; it just means that mine points out the boy and man better. Yours is fine, however, and it's a very good sentence.