garbage disposal unit sinktop flange is being very stubborn and won't come away
I had good luck removing a stubborn strainer once with a propane torch, heating the flange portion that sticks below the sink, then tapping at it occasionally with a hammer.

If you use a mapp gas torch, be aware that sucker will heat up fast. Try to stick to propane if you don't use mapp torches much.

Also, keep a close eye on things. You may not be fighting plumbers putty at all. Might be silicone in there from a past repair, or diy install.