Learn English – How does “off” fit in this sentence

Consider the following three sentences.

1. He raced out the door.
2. He raced out of the doorway.
3. He raced out of the door.

In the first sentence out is a preposition meaning 'through to the outside'. This is entirely unproblematic: he was in a room or building, and he raced out of it through the door(way).

In formal English the second sentence is equally clear: out is an adverb meaning 'moving or appearing to move away from a particular place, especially one that is enclosed', and the sentence means that he raced out of the doorway in which he had been standing. I shouldn’t be at all surprised, however, to find that some people use it synonymously with (1).

Since 'doorway' is one perfectly standard meaning of door, and since it is more than a little difficult to stand in a physical door, (3) is formally synonymous with (2). However, many people, evidently including at least one writer for Murder, She Wrote, use it synonymously with (1). For those people out of has in effect become a compound preposition meaning 'through to the outside' as well as the combination of adverb and preposition found in the formal interpretation of (2). I suspect that this, like in back of for behind, is more common in the US than in the UK. In the US, at least, it’s common enough to qualify as normal English, though there are also speakers like me who would never use it because it’s ungrammatical in their idiolects.

There's more than a hair's breadth of difference between these two statements!

The first simply means she had a haircut. Maybe she is now sporting a new style, or maybe she just had a trim.

The second means that her hair has been cut drastically short, if not completely shaved. It might be used if she once had very long hair, but, after her latest trip to the salon, it's now cut very short.

Note that the difference between cut and cut off can vary, depending on what's being cut.

She cut her finger means that she's bleeding, and may need to put a bandage on it. She cut her finger off means that, unless a doctor performs reattachment surgery, she'll only have four fingers for the rest of her life. He cut five pages from the back of the book might suggest an editor opted for a shorter ending. He cut off five pages from the back of the book could mean a bookbinder removed physical pages with an exacto knife.

For hair, however, she cut her hair is simply a common expression meaning she got a haircut. She cut her hair off suggests something far more drastic, which I've already explained.