Eine Scheibe Pizza
»Eine Scheibe« literally is a disc, i.e. a cylinder, where the diameter is much greater than the height.
Eine Scheibe:

This is called a »Scheibe« in German:
- CD or DVD
- vinyl record
- frisbee disc
- washer (lining disc)
- Planet Earth if you believe that it is flat
So, if you you use »Scheibe« in combination with »Pizza«, I would think ...
- Oh, thats a strange combination. It's pretty sure, that German is a foreign language for you.
- Probably you mean the hole pizza, because it has the shape of a disc. But that's really a very strange usage of »Scheibe«.
But there are also other meanings of »Scheibe«, derived from the disc-meaning:
A Scheibe is also the flat glass in a Window (although it's not round). I believe (but am not sure), that this is from those days when glass for windows was cut out of discs of hand-blown glass.
And, a Scheibe is also a slice that you cut off from a sausage or from Bread, sometimes also from cheese, because it looks like a disc (or at least almost).
conclusion:
Eine Scheibe Pizza
does not work in German. You will not be understood, or you will be understood wrong, and you will see questioning faces.
Ein Stück Pizza
»Ein Stück« is »a piece« in English. A Stück is one thing of many similar things.
When you cut a pizza into pieces (normally 8 pieces), then each of this 8 pieces is called »ein Stück Pizza«.
Ein Stück Pizza:

You use the German word »Stück« in the same situations when you use »piece« in English.
Eine Pizza
This is a complete pizza, i.e. that round thing, that comes out of an oven and can be cut into pieces.
Eine Pizza: