Honesty is the Best Policy Capitalize all or just the significant words in a title.

Once a woodcutter was cutting branches off a tree beside the by the bank of the a river. By Perchance his axe fell down into the water. As It was an irreparable loss for him. Therefore he started to weep and wept bitterly. The God of water the river took piety pity on him or compassionated on him and appeared before him as a man in form of human being and said

"My good fellow! Why are you dost weeping so bitterly?"

The woodcutter told the god related his tale of woe. The God dived dove into the water and came back with a golden axe.   and put it before him but The woodcutter refused to take it because as it was not his axe. Next time he god dove and returned came back with silver an axe of silver but he again refused to take it because accept as his axe was made of iron. Finally an axe of iron was brought back.  The woodcutter was overjoyed, Third time the god came back with iron axe. The woodcutter said,

"Yes! It is 'Tis my axe! I thank thee greatly."

The River God was so happy with his honesty and that he rewarded him with the other two axes.

You are writing a story.  Make it as interesting as possible and use the language more appropriately.  I am using an archaic language.  Won't look good if you use too modern a usage of the language, say current slang.

Honesty is the Best Policy

Once a woodcutter was cutting branches of a tree beside the the bank of the river. By chance, his axe fell down in the water. As It was an irreparable loss for him. Therefore, he started to weep bitterly. The god of water took piety pity on him or compassionated and compassion on him and appeared in the form of a human being and said, "Good fellow, why are you weeping?" The woodcutter told the god his tale of woe. The god dived into the water and came back with a golden axe and put it before him, but the woodcutter refused to take it because it was not his axe. Next The next time, the god came back with a silver axe, but he again refused to take it because his axe was made of iron. The third time the god came back with an iron axe. The woodcutter said, "Yes! It is my axe." The god was so happy with his honesty and that he rewarded him with the other two axes.

Honesty is the Best Policy

Once a woodcutter was cutting branches of a tree beside the the bank of the river. By chance, his axe fell down in the water. As It was an irreparable loss for him. Therefore, he started to weep bitterly. The god of water took piety pity on him or compassionated and compassion on him and appeared in the form of a human being and said, "Good fellow, why are you weeping?" The woodcutter told the god his tale of woe. The god dived into the water and came back with a golden axe and put it before him, but the woodcutter refused to take it because it was not his axe. Next The next time, the god came back with a silver axe, but he again refused to take it because his axe was made of iron. The third time the god came back with an iron axe. The woodcutter said, "Yes! It is my axe." The god was so happy with his honesty, and rewarded him with the other two axes.

Honesty is the best policy

This one is yours:

Once a woodcutter was cutting branches of a tree beside the the bank of the river. By chance his axe fell down in water. As it was a irreparable loss for him. Therefore he started to weep bitterly. The god of water took piety on him or compassionated on him and appeared in form of human being and said" Good fellow, why are you weeping?" The woodcutter told the god his tale of woe. The god dived into water and came back with a golden axe and put it before him but the woodcutter refused to take it because it was not his axe. Next time the god came back with silver axe but he again refused to take it because his axe made of iron. Third time the god came back with iron axe. The woodcutter said,"Yes! It is my axe." The god was so happy with his honesty and rewarded him with the other two axe.

Here are your corrections: 

Once a woodcutter was cutting branches of a tree beside the the bank of the river. By chance his axe fell down in water. As it was a irreparable loss for him. Therefore he started to weep bitterly. The god of water took pity on him or compassionated on him and appeared in form of human being and said" Good fellow, why are you weeping?" The woodcutter told the god his tale of woe. The god dove into water and came back with a golden axe and presented it before him, but the woodcutter refused to take it because it was not his axe. Next time, the god came back with silver axe but he again refused to take it because his axe made of iron. Third time the god came back with iron axe. The woodcutter said,"Yes! It is my axe." The god was so happy with his honesty and rewarded him with the other two axes.

Great job! I can tell that you are almost fluent. All you need to do is watch you tenses, (Past, Present, and Future) and your pluralization of words (Adding an "S" at the end of them).