I suspect the title of Margaret Mitchell's 1936 novel (and subsequent movie) was derived from the idiomatic expression, not the other way around. It's possible it was a local expression that came into widespread use with the popularity of the novel -- although, judging from the comments, "widespread" might still be somewhat limited.
Either way, it is an adjective phrase. It is used like other adjective phrases:
After the crash of the stock market in 1929, many families' life savings were gone with the wind.
"Gone" is the past participle of "go", and is generally used in the passive sense that the subject "no longer exists" rather than "went":
I know I put my phone on the bedside table last night, but when I woke up this morning it was gone!
The verb in the sentence is "was". You have to use a different word to suggest it was removed:
Someone must have taken it while I was sleeping!
Because it is passive "gone with the wind" deliberately avoids assigning fault to the result. It's as if a great windstorm came up out of nowhere and blew away some significant structure or achievement, and there was nothing anyone could have done to stop it. It is used metaphorically in the novel to describe the aftermath in the American South after the Civil War, where many of the old social and economic structures and customs (depicted in the first part of the story) were irrevocably changed.
For this reason it is difficult to replace with verbs like "squander", because these do imply fault. Similarly other verbs like "annihilate" or "demolish" suggest human action rather than natural forces.
There is really no easy way to turn the expression into a verb without changing the meaning. It is possible to say something like:
The family fortune went with the wind
The family fortune blew away with the wind
the family fortune was blown away by the wind
but these just play off of the idiomatic expression, and may be awkward if not framed by an appropriate reference.
If I had to pick a single word closest to the meaning, I would use "evaporate", because this is a natural action that no human effort can stop.
It is not entirely clear how the fortunes of the family evaporated over the generations, but eventually the famous author's descendants were left nothing but her renowned name.
However "evaporate" implies a gradual, steady action, rather than one that is sudden and violent.
Side note: Even though "gone with the wind" might not be used, the meaning is pretty self-apparent, unlike other English idioms which range from the inscrutable ("the bee's knees") to the ambiguous ("a dog's life").