Yes, the whole thing will have to come out which means you will likely need to finish the floor under it because it is probably not finished if it was installed when the house was built.

This video is not exactly the same type as you describe but sounds similar and may be helpful https://www.hometalk.com/27734574/removing-a-corner-steeping-bath-tub

Removing a Corner Steeping Bath Tub

Hi Thelma, we recently just did this exact thing. The jets worked but were icky. There was no way to remedy it except to remove the entire tub. It turned out to be a bigger job than expected because we lost some of the wall tile and there is a hole in the floor under the tub for the motor etc. Here's a bit of our tale. https://www.exquisitelyunremarkable.com/2019/04/a-fine-mess.html

https://www.hometalk.com/37057948/q-removing-jetted-tub-and-replacing-with-freestanding-tub

Cut the tub up into pieces with a reciprocating saw and in about a half an hour, the white elephant in the room will be gone. Yes, the finishing of the walls and floor afterwards is a a job, but when you see what a huge space it will give, you will wonder why you didn't get rid of it 10 years ago.

I don't think there is a safe way to do it. You may want to plug it only

If you remove it, do you have a replacement? You would be better plugging it, if not.

I think removing it is a safe way to go! Here is a great post on removing a jetted tub safely.

https://www.hunker.com/13400879/how-to-remove-jet-tubs