Is it "I cut my hair myself" or "I cut my hair by myself" or "I cut my hair"?
Which one of the three is grammatically correct?
Each one of those sentences has a different implication although they all could give the same meaning which is doing something alone.
The first one is used when you want to imply that you are the only one who cut his hair.
The second sentence implies you cut your hair without anyone helping you.
The last one is kind of ambiguous. You are just saying you did cut your hair. There could be someone that helped, cut it for you or did the same thing to himself. No implications.
To make something shorter by cutting trans.without the help of anyone else.
All the sentences are correct grammatically, with a little difference in meaning. As the past of the verb cut is also cut, these sentences may be in the present or past simple. Let's think they are in the present simple.
You use the verb cut for hair to mean "make your hair shorter by cutting".
If you cut your hair, it may mean that you cut your hair with or without the help of another person; the sentence is ambiguous.
If you cut your hair yourself, it means the same thing as above, but there's an emphasis on your doing it.
If you cut your hair by yourself, it's quite clear that you cut your hair yourself without the help of anybody else.
Out of the three, the best option is:
I cut my hair by myself.
It sounds the best. It gives the complete information. Additionally, take the following sentence,
I cut my hair once every year.
Now, this means that the subject gets a haircut once in a year. But that doesn't mean he does it himself. He could get it cut by a hair stylist, or whoever it maybe. So the third option need not mean the same as the first two.
PS: I would advice you not to use the example I suggested. But I only used that to explain the context. The best way to use the example I suggested would be 'I get a haircut once every year'.