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There are lots of varieties of potato that cover a large range of starch content, sweetness, flavors and textures. The type of potato used will be a bigger influence on the final dish than the way in which they are cut.

That said, the technique you describe (incomplete cutting followed by ripping) will release more starch from each potato than if they were completely cut. Cuts made with a sharp knife rupture fewer cells. The more free-floating starch can affect the texture of the dish, and frying the released starch will tend to increase the Maillard reactions, which will change the flavor to a deeper, more complex profile.

Similar effects could be obtained by smashing some of the potato slices, or treating them more roughly in the pan, or by using a different variety of potato with more starch.