I removed a sole plate and there is a heavy duty nail or anchor sticking up about an inch. It looks different from a regular nail but it has to be removed to continue with flooring at the same level of the previously installed tile which is going to be repaired and installed to complete the project. How should I remove?

Hammer it over to one side, it will break off.

Use a right angle grinder and cut off flush with floor.

Chuck

If it is a nail, bend it back and forth till it breaks, if it is a bolt, use a sawzall and a metal cutting blade. Even if it scars up the floor, you will be covering it.