The name Krittika comes from the act of cutting. Its two symbols say the same thing in different ways. A blade divides. Fire burns. Both separate what should stay from what should go.
Its shakti (the special power a nakshatra carries) is burning and purification. Fire does two jobs here. Think of it in your own kitchen. The same flame that can burn your hand is the one that cooks your dinner. Agni is present at the stove and at the cremation ground. So Krittika is never only about cutting things away.
In Hindu mythology, the Krittikas are six mothers who nursed the infant Kartikeya, also called Skanda or Murugan. He is the son of Shiva, and he grew up to lead the armies of the gods. Those six mothers are the six stars of the Pleiades, the cluster this nakshatra is named after. In Tamil Nadu, the festival of Karthigai Deepam, when rows of lamps are lit, is tied to this same star.
That story changes how you read the nakshatra. Krittika is known for sharpness, but it is equally known for raising and protecting. These are the people who will tear your business plan apart on Monday and then spend Saturday helping you rewrite it.
Krittika is also known for a fast, precise mind. You will see it in the person who catches the error nobody else caught. They can tell a good mango from a bad one at a glance. They pick up a new skill by watching someone do it once. Fire gives heat, and here that heat shows up as focus.