Using a preset animation:
So create preset animation in a 3D modelling software like Maya/Blender which has features like soft bodies and cloth that can do a good job simulating the pizza tearing. Export both the pizza texture AND the model animation to Unity (probably as a set of .obj models or some such).
The model animation will represent the cheese being stretched and torn using many many triangles, which you can load as a set of tri-meshes into Unity. They are collection of many mesh states, each representing the cheese pizza at different positions of stretching. Based on where the user positions the pizza slice, you'll jump to that 'mesh state' and display those triangles.
There're a few problems of-course. The user interaction is a bit restricted. If cheese is already torn a bit, you can't go back to 'untorn' state for that area of cheese. If the preset animation removes slice 1 and then 2, the user will be forced to remove the slices in that order. The size of data exported can become pretty big, based on how granular the mesh is and how long the tearing animation lasts.
But it can look very realistic, if the model artist does a good job when creating the preset animation. And you don't have to implement a soft-body simulator.
But in-case you're interested Unity does implement its own Skinned cloth and Interactive cloth components. The interactive cloth supports tearing. But support for them are restricted to only a few platforms, last I checked.
In the end, you can always implement your own soft-body simulator. Here's a sample research paper that's pretty popular. It is a lot of fun :). Good luck.