Two words you could use are "rewrite" and "Edit."
Use Rewrite if you must fix all or part of a paper/document.
Use edit if you need to fix spelling, punctuation, or a few sentences.
Examples
Rewrite - My boss did not like the article and asked me to rewrite the entire thing.
Could you rewrite the final paragraph of this blogpost, please?
Edit - I had to edit a few sentences, but overall it was a great article.
Go through and edit the spelling mistakes I noted.
"Rewrite" と "Edit" という二つの単語が使えます。
"Rewrite" は、論文や文書の全てあるいは一部を直すときに使います。
"Edit" は、スペルや句読点、文章をいくつか直すときに使います。
例：
［Rewrite］
My boss did not like the article and asked me to rewrite the entire thing.（上司がその記事を気に入らなくて、丸々書き直してくれと頼まれた）
Could you rewrite the final paragraph of this blogpost, please?（このブログ記事の最後の段落を書き直してもらえますか）
［Edit］
I had to edit a few sentences, but overall it was a great article.（いくつか文章を直しましたが全体として素晴らしい記事でした）
Go through and edit the spelling mistakes I noted.（確認して指摘したスペルミスを直してください）
A word that means to "write again so as to alter/improve it"or in Japanese "kakinaosu" could be one of the above suggestions, depending on the context.
Eg.. 'Max edited his dissertation to take account of recent research.'
Eg. 'The actor's lines were updated by the director.'
Eg. 'You should rewrite your speech so it is more empathetic towards minority groups.'
日本語の「書き直す（一度書いたものをより良くなるように書き換えること）」は、文脈によって上記のように訳せるかもしれません。
例：'Max edited his dissertation to take account of recent research.'（マックスは最近の研究を踏まえて論文を書き直した）
例：'The actor's lines were updated by the director.'（その俳優のセリフは監督によって書き直された）
例：'You should rewrite your speech so it is more empathetic towards minority groups.'（演説を少数派に配慮した内容に書き換えるべきです）
In American English, we use both of these terms to talk about rewriting something in order to change its character in some way. We might edit a text for content, tone, grammar, spelling, punctuation, etc. We often talk about making 'edits' or 'corrections' to a document in order to improve it in various ways. A person who does this sort of thing professionally is often referred to as an 'Editor' or perhaps 'Proofreader' (which is a more technical job). I hope that this is useful to you.
None of us are perfect and we all make spelling mistakes, some of us use spellcheck on our computers and others use spelling applications, but we all need help, even if we are really good at spelling words. Spellchecks doesn't just help with spelling, it also helps with grammar and punctuation.
"I need to revise my presentation!
"I think that I have to reword my essay!"
"I might have to rephrase this letter!
世の中に完璧な人はおらず、誰しもつづりの間違いを犯します。パソコンのスペルチェッカーを使う人もいればスペルチェックのアプリを使う人もいます。いずれにしても、たとえ単語のつづりがすごく得意な人でも、何かしらの助けは必要です。スペルチェッカーは単語のつづりに限らず文法や句読点についても正してくれます。
"I need to revise my presentation!"（プレゼンテーションを変更しないといけない）
"I think that I have to reword my essay!"（エッセーを書き換えないといけないと思う）
"I might have to rephrase this letter!"（この手紙を書き直さないといけないかもしれない）
Rewrite and Rephrase are used in a similar context, to improve a sentence or word
"Let me rewrite this paragraph" "Let me rephrase this sentence"
"correct" more used when something is wrong "Let me correct the spelling and grammar of this sentence"
"Rewrite" と "Rephrase" は同じような文脈で使われます。言葉や文章を改善することをいいます。
例：
"Let me rewrite this paragraph"（この段落を書き直します）
"Let me rephrase this sentence"（この文を言い換えましょう）
"Correct" は何かが間違っているときに使われます。
例：
"Let me correct the spelling and grammar of this sentence"（この文のスペルと文法を直しましょう）
We all make mistakes sometimes so we might need to re-do something this simply means to do it all over again if w make a mistake or it is not quite right
If we need to write something out again we say we will 'rewrite it' so 'I had to rewrite my essay today'
to edit something means to change it as it's not right
私たちは皆ミスをしますね。時に 're-do' しなければならないこともあるかもしれません。're-do' は「（ミスがある、適切でないなどの理由で）最初からやり直す」という意味です。
何かをもう一度書き直すことは、'rewrite' といいます。
例えば：
'I had to rewrite my essay today'（今日はエッセーを書き直さないといけませんでした）
'edit' は「適切でないものを変更する」という意味です。
The word "rewrite" can be used to express to someone that they should write what they previously wrote again. It's often used in situations when there has been a mistake made in the previous writing.
「書き直す」という言葉を英語で表すと、「rewrite」と「edit」または「revise」になります。例えば、「I had to rewrite my essay because there were so many mistakes in it.」という文章を使っても良いと考えました。「I had to ~ .」は「私は〜をしなければならなかった」という意味があって、「essay」は「作文」という意味があります。「Mistake」は「間違い」という意味があります。
日本 
アメリカ合衆国 
イギリス 
南アフリカ 
