The meat cutting was realized by generating a cylindric set of sphere collision components around the kebab mesh from the bottom up. In this video you can see some of the settings available to our game designers which could be used to control how much meat pieces would be on the kebab spit.
The meat cutting was then simply a matter of overlap checks with these generated collision components enhanced by some visual and haptic feedback.

Of course meat must be properly cooked before it can be cut-off and served. This process of meat-cooking can be clearly observed when enabling the color-sphere debug visualization. The spheres gradually increase in "cookedness" from red to green over a course of round about 30 seconds. After a piece of meat was cut-off, the corresponding meat-sphere needs to recharge, so it can be cut again.

The kebab material used a simple paint effect utilizing dynamic rendertargets to blend between cooked and uncooked meat material layers. While cooking the mask was gradually darkened, whereas cutting the meat off would paint a white circle brush onto the texture mask.
The material excerpts below show the paint material that is used to paint out areas that are cut off the kebab. During every frame in which the cutting tool comes close enough to the kebab, we make a UV trace from the cutter onto the kebab mesh to find out at which UV to make a brush stroke onto the render target. This brush is then only applied additvely for pixels that are dark/cooked enough to warrant cutting away meat. This value is synchronized with the minimum cookedness that is used for the logical meat spheres that were described above.
This design doesn't enforce a synchronization between the game logic and visualization, instead they just happend to line up.