Like the tutorial says; when time slows down a little bit you can enter Blade Mode, allowing you to slice through enemies. You can manually angle the cut using right stick; flicking it, and pan using left stick. If you don't care to do that, you can press 'X' for horizontal attacks or 'Y' for vertical slices. It it worthy to note that it is faster to use 'X' and 'Y', but if you manage to sever a limb entirely (not into little pieces), it will yield extra points; which adds up over time.
Additionally, some enemies will not die from egregious maimage, so your best bet is to always aim for the red square.