When I install vinyl, I always suggest to homeowners that they not go with sheet vinyl. Sure it looks nicer and void of those seams, but wonder if you drop a knife and the blade tears a hole in the flooring. With sheet, you are out of luck, with squares, just remove the damaged square, clean off the subsurface and apply a new square. you are set.
If you have squares, start in the middle and chissle out the bad square being careful not to damage the corners of the adjoining square. Get a putty knife and clean off any gunk off the below floor. Then remove the backing of your new tile and find the laying order and place it down and put some books on top of that square for the night.
I do hope that your situation is the latter.
This is solely my opinion and others may have different procedures and methods.