Deleted Scenes
Mothra (1961)

Saving Shinji
With Professor Chujo's son, Shinji, still kidnapped, Nelson attempts to flee with the Shobijin in a small private plane, before it crashes near a mountainside. Armed, Nelson and his entourage trek up the mountain as Senichiro Fukuda and the authorities give chase. They manage to secure Shinji away from Nelson just as Mothra is seen flying in the distance.

The original climax for Mothra was entirely different from what ended up in the final print. Originally, Nelson and his group had planned to kidnap Shinji Chujo for a longer period of time, rather then leaving him tied up as they fled the country. Instead, they took the small boy on a private plane as they attempted to flee, only to accidentally crash near a mountainside. Meanwhile, the film's heroes are in close pursuit, having brought along the authorities to help save the boy. All of this takes place while Mothra is still in its cocoon, meaning that Fukuda and the others weren't originally planned to witness the birth of Mothra's Imago form. Instead they give chase to Nelson as Mothra breaks free after the Atomic Ray Gun attack. She then immediately flies to the mountainside after the Shobijin.

It's hard to say how much of the original climax was finished before being cut, but there are a number of black and white production stills showing that the mountain chase sequence was filmed, at least in part; however, no photos have been seen of the story boarded sequence relating to the plane crash that would have occurred just before it.

Mothra Kills Nelson
As Nelson and his group are chased up into the mountains, Mothra arrives to save the Shobijin. Despite Nelson's efforts, the giant insect manages to force him off a cliff where he plummets to his death.

The original end of the film had Mothra actually sending Nelson off the mountain to his demise, as she personally would have saved the Shobijin.

This scene, and a lot of events that led up to it, where all eventually cut from the movie when Columbia purchased some of the overseas distribution rights. The extra money from this was used to greatly increase the involvement of the Imago form in the movie, making Nelson flee to the mythical country of Rolisica so that Mothra can decimate the city in her pursuit of the Shobijin. Consequently, the entire climax had to be altered to fit, causing for a huge change from the original story.

In terms of how much of it was filmed, it's hard to say. There were certainly a number of black and white production stills in existence that relate to Nelson and his group gaping in horror as Mothra approached them. In fact, the primary poster for the film even features a shot of Nelson screaming in terror, which was originally part of this sequence. So it definitely seems that the actor part was filmed, although it seems less likely that the Mothra portion was ever completed.