Tricky Faucet Replacement

Hi everyone. I'm a DIY'er hoping to get some advice on uninstalling a faucet, so please forgive if I do not use the proper terminology. I really appreciate your time and any advice you can provide.

The tricky part is how the faucet was originally attached. My sink is a 3-hole sink like the one in the link below:

https://www.plumbersstock.com/images/products/large/00364617.jpg

When the faucet was originally installed, the 2 outer holes had bolts coming down from the top with a plastic threaded washer/nut on the bottom to tighten and secure the faucet base plate to the sink. As far as I can tell, the people who installed it used plumber's putty or some other kind of adhesive to bond the wide and flat surface of the plastic washer/nut to the bottom of the sink. Because of this, I am unable to unscrew these and remove the faucet. I was able to break the seal, but still cannot unscrew the washer/nut.

I'm thinking that my only option at this point is to take a dremel to the plastic washer/nut and bolt to cut them loose. Any advice would be greatly appreciated. If more information is required, I'll gladly provide what I can. Thanks in advance!

Yes, breaking the nut is how to do it. A dremel should work. I often use a sharp chisel, but you have to be careful not to "ding" the sink.

Sound like they used putty on top of the sink, but uses so much that it squeezed down through the hole

A hot screwdriver will work as well.