From time to time, the death penalty in japan has been questionedhas been debated in Japan.

Debate implies discussion on both sides, but it's just a more idiomatic word for this context too.

Even though it has been under fire from the international human rights groups, the Japanese government haves not abolished it and Japanese people are still permissive towardsfavor it.

Government is singular so you need 'has' not 'have'.
'Permissive' sounds like they just tolerate it, but in the next sentences you say 80% are in favor of it.

When they were asked why (or 'for a reason'), they replied, "if it were not for the death penalty, the victims and their family members cannotould be at peace."

I believe there is another way, but I also think that that is what it is.

I don't understand this. You say there is another way, but then -- what? are you talking about the other way?

Though resentment of victims cannot disappear, the punishment will bepunishment cannot erase the grief of the victims, it may bring them a kind of relief to them.

Resentment is the wrong word. It's too mild for the reaction of victims of violent crimes. Grief or trauma, maybe.

I think the death penalty is not the best way to punish convicts, but it is still necessary.

Way as used here is a pronoun, but you haven't been explicit about what it refers to. This correction improves clarity.

From time to time, the death penalty in jJapan has been questioned.

Countries are always capitalized

Even though it has been under fire from the international human rights groups, the Japanese government haves not abolished it and Japanese people are still permissive towardsaccepting of it.

"permissive towards" is not incorrect. Accepting of it is a much more common phrasing however.

A poll conducted in 2014 shows that almost 80 per cent of the people think "the death penalty is inevitable."

you don't need "the" here.

Inevitable is a strange word choice. I would suggest something like required or obliged. I have left it because it is a quotation.

When they were asked a reason, they replied, "if it were not for the death penalty, the victims and their family members cannot be at peace."

I believe there is another way, but I also think that that it is what it is.