Thanks for this essay on what really is a controversial topic. But I’m very glad you didn’t use those words in your intro.

Introduction

Good, simple, and clear. Well done. Here’s a slight rewrite:

Although many countries have stopped using it, capital punishment has been implemented by some countries for many years. However, some nations are currently considering whether to re-introduce that punishment or not. This essay will address two important points that support the use of the death penalty.

Avoid generalizations

It’s OK to give your opinion in Task 2. That’s what the question asks you to do. And even if the examiner doesn’t agree with you, he or she will give you a mark based on how you express and develop your ideas.

However, it’s no harm to present your ideas in a way that does not actually annoy or irritate an examiner. There’s a very useful set of suggestions by Donna Millen here on the IELTS-Blog.com website. It’s taken from the book IELTS on Track.

According to religion, people should receive what they have done to others

This may be true for you. But what if the examiner is not of your religion, or is of a religion that has a different belief? Or does not have any religious beliefs at all?

It’s easy. Don’t change your opinion. Just soften it. Use modals (can, may, possibly, might, could). Use ‘most’ or ‘many’ instead of ‘all,’ ‘some’ instead of ‘everyone.’ You can also be specific -  say ‘in my country,’ ‘in my religion,’ etc.

• According to most world religions, people should be treated in the same way they treat others.
• The Christian Old Testament asks for an eye for an eye and a tooth for a tooth.
• Most Christians and Muslims believe that the punishment should fit the crime.
• As a [insert religion here], I believe that...

The point is not that the examiner is right and you are wrong, or vice versa. The point is that the IELTS test measures your ability to express your opinions in English in a certain way.  This way of presenting opinions may differ from culture to culture, but IELTS has its own cultural and academic setting.

Word Choice/Usage

• The capital punishment will rise more people’s awareness of law. →
  The capital punishment will increase more people’s awareness of law.
• The stronger punishment will remind citizens for not to infringe the society regulation →
  The stronger punishment will remind citizens not to infringe society’s regulations
• On the contrary, if the rule is not strong enough, people so that would break the law easily as they will not get severe charged →
  On the contrary, if the rule is not strong enough, people would break the law frequently as they would not be charged severely

Word Count

The big problem is that while the essay is well organized, it's too short. You HAVE to reach 240. Why not give the other side in this essay? One short paragraph would bring up to 260 words or more.

There are several reasons why the death penalty is not being used in some countries. Some people are afraid that innocent people will be executed. This is certainly possible, but with a good judicial system and with appeals and safeguards, this should be absolutely minimized. Another reason often given is that executing someone, for example, for murder, is just repeating the crime. We are no better than the criminal. However, this is just cowardice. If we don't take action to protect societies, the victims will have died in vain. Finally...

You could add a paragraph like this after the introduction, and THEN have your two paragraphs in favor of capital punishment. Have a look at Kenny's question here.

According to religion, people should receive what they have done to others. It teach us to do good things so that we will get good thing in return. But if we make bad thing, it must fetch that back to us. Therefore when anyone commit crimes as worth as a human life,  that man have to compensate for that with his own life. For example, committing murder, the murderer have to be sentenced to death to pay for whom he has killed.

The capital punishment will rise more people’s awareness of law. The stronger punishment will remind citizens for not to infringe the society regulation as they realize what punishment they will experience. On the contrary, if the rule is not strong enough, people so that would break the law easily as they will not get severe charged. The law therefore should be concrete in terms of punishment like death sentence.

Capital punishment is needed to keep people’s more awareness of legal behavior and it is human morality to get what we have done.

216 words