How could you mine underneath it without drowning? Even if you could it would 99% stay in place just like several other 'permanent items. Rune stones, troll caves, etc.
I was wanting to build under the Elder altar but the first one I found was just sitting on the water table like yours. I searched around for some time for another and found one that worked out well.

https://steamcommunity.com/sharedfiles/filedetails/?id=2811747084

https://steamcommunity.com/sharedfiles/filedetails/?id=2810249936

Originally posted by DezNutz:

what would happen if I did mine all around it. Would it float in the air? or would it be destroyed?

Yes, it would float. Anything like a boss altar, or cave entrance, or even some rock formations are not destroyable and will just float if you dig under them.

Thank you for the replies, I was just apprehensive to try it . I will throw up a screen shot next time i log on.